initial commit of all data

8 files changed, 777 insertions, 0 deletions

diff --git a/src/Hamming/Hamming.c b/src/Hamming/Hamming.c
new file mode 100644
index 0000000..cb1fba3
--- /dev/null
+++ b/src/Hamming/Hamming.c
@@ -0,0 +1,174 @@
+/*
+Hamming Error-Correcting Code (ECC)
+Optimized for avr-gcc 4.8.1 in Atmel AVR Studio 6.2
+August 12, 2014
+
+You should include Hamming.c, Hamming.h, and only one of the other Hamming files in your project.
+The other Hamming files implement the same methods in different ways, that may be better or worse for your needs.
+
+This was created for LoFi in the TheHackadayPrize contest.
+http://hackaday.io/project/1552-LoFi
+
+Copyright 2014 David Cook
+RobotRoom.com
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include <avr/pgmspace.h>
+
+#include "Hamming.h"
+
+/****************************/
+/*                          */
+/* Constants and structures */
+/*                          */
+/****************************/
+
+#ifndef null
+#define null ((void*) 0)
+#endif
+
+// If transmitting/writing only, you don't need to include this file.
+// If receiving/reading, then this provides the methods to correct bit errors.
+
+#define UNCORRECTABLE	0xFF
+#define ERROR_IN_PARITY	0xFE
+#define NO_ERROR		0x00
+
+
+/****************************/
+/*                          */
+/*     Global variables     */
+/*                          */
+/****************************/
+
+// Private table. Faster and more compact than multiple if statements.
+static const byte _hammingCorrect128Syndrome[16] PROGMEM =
+{
+	NO_ERROR,			// 0
+	ERROR_IN_PARITY,	// 1
+	ERROR_IN_PARITY,	// 2
+	0x01,				// 3
+	ERROR_IN_PARITY,	// 4
+	0x02,				// 5
+	0x04,				// 6
+	0x08,				// 7
+	ERROR_IN_PARITY,	// 8
+	0x10,				// 9
+	0x20,				// 10
+	0x40,				// 11
+	0x80,				// 12
+	UNCORRECTABLE,		// 13
+	UNCORRECTABLE,		// 14
+	UNCORRECTABLE,		// 15
+};
+
+/****************************/
+/*                          */
+/*      Private methods     */
+/*                          */
+/****************************/
+
+// Give a pointer to a received byte,
+// and given a nibble difference in parity (parity ^ calculated parity)
+// this will correct the received byte value if possible.
+// It returns the number of bits corrected:
+// 0 means no errors
+// 1 means one corrected error
+// 3 means corrections not possible
+static byte HammingCorrect128Syndrome(byte* value, byte syndrome)
+{
+	// Using only the lower nibble (& 0x0F), look up the bit
+	// to correct in a table
+	byte correction = pgm_read_byte(&(_hammingCorrect128Syndrome[syndrome & 0x0F]));
+
+	if (correction != NO_ERROR)
+	{
+		if (correction == UNCORRECTABLE || value == null)
+		{
+			return 3; // Non-recoverable error
+		}
+		else
+		{
+			if ( correction != ERROR_IN_PARITY)
+			{
+				*value ^= correction;
+			}
+
+			return 1; // 1-bit recoverable error;
+		}
+	}
+
+	return 0; // No errors
+}
+
+
+/****************************/
+/*                          */
+/*      Public  methods     */
+/*                          */
+/****************************/
+
+// Given a pointer to a received byte and the received parity (as a lower nibble),
+// this calculates what the parity should be and fixes the received value if needed.
+// It returns the number of bits corrected:
+// 0 means no errors
+// 1 means one corrected error
+// 3 means corrections not possible
+byte HammingCorrect128(byte* value, nibble parity)
+{
+	byte syndrome;
+
+	if (value == null)
+	{
+		return 3; // Non-recoverable error
+	}
+
+	syndrome = HammingCalculateParity128(*value) ^ parity;
+
+	if (syndrome != 0)
+	{
+		return HammingCorrect128Syndrome(value, syndrome);
+	}
+
+	return 0; // No errors
+}
+
+
+// Given a pointer to a first value and a pointer to a second value and
+// their combined given parity (lower nibble first parity, upper nibble second parity),
+// this calculates what the parity should be and fixes the values if needed.
+// It returns the number of bits corrected:
+// 0 means no errors
+// 1 means one corrected error
+// 2 means two corrected errors
+// 3 means corrections not possible
+byte HammingCorrect2416(byte* first, byte* second, byte parity)
+{
+	byte syndrome;
+
+	if (first == null || second == null)
+	{
+		return 3; // Non-recoverable error
+	}
+
+	syndrome = HammingCalculateParity2416(*first, *second) ^ parity;
+
+	if (syndrome != 0)
+	{
+		return HammingCorrect128Syndrome(first, syndrome) + HammingCorrect128Syndrome(second, syndrome >> 4);
+	}
+
+	return 0; // No errors
+}
diff --git a/src/Hamming/Hamming.h b/src/Hamming/Hamming.h
new file mode 100644
index 0000000..7778a59
--- /dev/null
+++ b/src/Hamming/Hamming.h
@@ -0,0 +1,68 @@
+/*
+Hamming Error-Correcting Code (ECC)
+Optimized for avr-gcc 4.8.1 in Atmel AVR Studio 6.2
+August 12, 2014
+
+You should include Hamming.c, Hamming.h, and only one of the other Hamming files in your project.
+The other Hamming files implement the same methods in different ways, that may be better or worse for your needs.
+
+This was created for LoFi in the TheHackadayPrize contest.
+http://hackaday.io/project/1552-LoFi
+
+Copyright 2014 David Cook
+RobotRoom.com
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#ifndef _HAMMING_H
+#define _HAMMING_H
+
+#ifndef _AVR_H
+typedef unsigned char byte;
+typedef unsigned char nibble;
+#endif
+
+/**** These are needed to transmit and receive ****/
+
+// Given a byte to transmit, this returns the parity as a nibble
+nibble HammingCalculateParity128(byte value);
+
+// Given two bytes to transmit, this returns the parity
+// as a byte with the lower nibble being for the first byte,
+// and the upper nibble being for the second byte.
+byte HammingCalculateParity2416(byte first, byte second);
+
+
+
+/**** These are needed only to receive ****/
+
+// Given a pointer to a received byte and the received parity (as a lower nibble),
+// this calculates what the parity should be and fixes the received value if needed.
+// It returns the number of bits corrected:
+// 0 means no errors
+// 1 means one corrected error
+// 3 means corrections not possible
+byte HammingCorrect128(byte* value, nibble parity);
+
+// Given a pointer to a first value and a pointer to a second value and
+// their combined given parity (lower nibble first parity, upper nibble second parity),
+// this calculates what the parity should be and fixes the values if needed.
+// It returns the number of bits corrected:
+// 0 means no errors
+// 1 means one corrected error
+// 2 means two corrected errors
+// 3 means corrections not possible
+byte HammingCorrect2416(byte* first, byte* second, byte parity);
+
+#endif // _HAMMING_H
diff --git a/src/Hamming/HammingCalculateParityFast.c b/src/Hamming/HammingCalculateParityFast.c
new file mode 100644
index 0000000..6cc5df6
--- /dev/null
+++ b/src/Hamming/HammingCalculateParityFast.c
@@ -0,0 +1,67 @@
+/*
+Hamming Error-Correcting Code (ECC)
+Optimized for avr-gcc 4.8.1 in Atmel AVR Studio 6.2
+August 12, 2014
+
+You should include Hamming.c, Hamming.h, and only one of the other Hamming files in your project.
+The other Hamming files implement the same methods in different ways, that may be better or worse for your needs.
+
+This was created for LoFi in the TheHackadayPrize contest.
+http://hackaday.io/project/1552-LoFi
+
+Copyright 2014 David Cook
+RobotRoom.com
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include <avr/pgmspace.h>
+
+#include "Hamming.h"
+
+
+// This contains all of the precalculated parity values for a byte (8 bits).
+// This is very fast, but takes up more program space than calculating on the fly.
+static const byte _hammingCalculateParityFast128[256] PROGMEM =
+{
+	 0,  3,  5,  6,  6,  5,  3,  0,  7,  4,  2,  1,  1,  2,  4,  7,
+	 9, 10, 12, 15, 15, 12, 10,  9, 14, 13, 11,  8,  8, 11, 13, 14,
+	10,  9, 15, 12, 12, 15,  9, 10, 13, 14,  8, 11, 11,  8, 14, 13,
+	 3,  0,  6,  5,  5,  6,  0,  3,  4,  7,  1,  2,  2,  1,  7,  4,
+	11,  8, 14, 13, 13, 14,  8, 11, 12, 15,  9, 10, 10,  9, 15, 12,
+	 2,  1,  7,  4,  4,  7,  1,  2,  5,  6,  0,  3,  3,  0,  6,  5,
+	 1,  2,  4,  7,  7,  4,  2,  1,  6,  5,  3,  0,  0,  3,  5,  6,
+	 8, 11, 13, 14, 14, 13, 11,  8, 15, 12, 10,  9,  9, 10, 12, 15,
+	12, 15,  9, 10, 10,  9, 15, 12, 11,  8, 14, 13, 13, 14,  8, 11,
+	 5,  6,  0,  3,  3,  0,  6,  5,  2,  1,  7,  4,  4,  7,  1,  2,
+	 6,  5,  3,  0,  0,  3,  5,  6,  1,  2,  4,  7,  7,  4,  2,  1,
+	15, 12, 10,  9,  9, 10, 12, 15,  8, 11, 13, 14, 14, 13, 11,  8,
+	 7,  4,  2,  1,  1,  2,  4,  7,  0,  3,  5,  6,  6,  5,  3,  0,
+	14, 13, 11,  8,  8, 11, 13, 14,  9, 10, 12, 15, 15, 12, 10,  9,
+	13, 14,  8, 11, 11,  8, 14, 13, 10,  9, 15, 12, 12, 15,  9, 10,
+	 4,  7,  1,  2,  2,  1,  7,  4,  3,  0,  6,  5,  5,  6,  0,  3,
+};
+
+// Given a byte to transmit, this returns the parity as a nibble
+nibble HammingCalculateParity128(byte value)
+{
+	return pgm_read_byte(&(_hammingCalculateParityFast128[value]));
+}
+
+// Given two bytes to transmit, this returns the parity
+// as a byte with the lower nibble being for the first byte,
+// and the upper nibble being for the second byte.
+byte HammingCalculateParity2416(byte first, byte second)
+{
+	return (pgm_read_byte(&(_hammingCalculateParityFast128[second]))<<4) | pgm_read_byte(&(_hammingCalculateParityFast128[first]));
+}
diff --git a/src/Hamming/HammingCalculateParitySmall.c b/src/Hamming/HammingCalculateParitySmall.c
new file mode 100644
index 0000000..d446f8f
--- /dev/null
+++ b/src/Hamming/HammingCalculateParitySmall.c
@@ -0,0 +1,99 @@
+/*
+Hamming Error-Correcting Code (ECC)
+Optimized for avr-gcc 4.8.1 in Atmel AVR Studio 6.2
+August 12, 2014
+
+You should include Hamming.c, Hamming.h, and only one of the other Hamming files in your project.
+The other Hamming files implement the same methods in different ways, that may be better or worse for your needs.
+
+This was created for LoFi in the TheHackadayPrize contest.
+http://hackaday.io/project/1552-LoFi
+
+Copyright 2014 David Cook
+RobotRoom.com
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "Hamming.h"
+
+/****************************/
+/*                          */
+/*      Public  methods     */
+/*                          */
+/****************************/
+
+// This is slower than using a table, but faster than
+// using the textbook method.
+
+// Given a byte to transmit, this returns the parity as a nibble
+nibble HammingCalculateParity128(byte value)
+{
+	// Exclusive OR is associative and commutative, so order of operations and values does not matter.
+	nibble parity;
+
+	if ( ( value & 1 ) != 0 )
+	{
+		parity = 0x3;
+	}
+	else
+	{
+		parity = 0x0;
+	}
+
+	if ( ( value & 2 ) != 0 )
+	{
+		parity ^= 0x5;
+	}
+
+	if ( ( value & 4 ) != 0 )
+	{
+		parity ^= 0x6;
+	}
+
+	if ( ( value & 8 ) != 0 )
+	{
+		parity ^= 0x7;
+	}
+
+	if ( ( value & 16 ) != 0 )
+	{
+		parity ^= 0x9;
+	}
+
+	if ( ( value & 32 ) != 0 )
+	{
+		parity ^= 0xA;
+	}
+
+	if ( ( value & 64 ) != 0 )
+	{
+		parity ^= 0xB;
+	}
+
+	if ( ( value & 128 ) != 0 )
+	{
+		parity ^= 0xC;
+	}
+
+	return parity;
+}
+
+// Given two bytes to transmit, this returns the parity
+// as a byte with the lower nibble being for the first byte,
+// and the upper nibble being for the second byte.
+byte HammingCalculateParity2416(byte first, byte second)
+{
+	return (HammingCalculateParity128(second) << 4) | HammingCalculateParity128(first);
+}
+
diff --git a/src/Hamming/HammingCalculateParitySmallAndFast.c b/src/Hamming/HammingCalculateParitySmallAndFast.c
new file mode 100644
index 0000000..ad27bf8
--- /dev/null
+++ b/src/Hamming/HammingCalculateParitySmallAndFast.c
@@ -0,0 +1,64 @@
+/*
+Hamming Error-Correcting Code (ECC)
+Optimized for avr-gcc 4.8.1 in Atmel AVR Studio 6.2
+August 12, 2014
+
+You should include Hamming.c, Hamming.h, and only one of the other Hamming files in your project.
+The other Hamming files implement the same methods in different ways, that may be better or worse for your needs.
+
+This was created for LoFi in the TheHackadayPrize contest.
+http://hackaday.io/project/1552-LoFi
+
+Copyright 2014 David Cook
+RobotRoom.com
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include <avr/pgmspace.h>
+
+#include "Hamming.h"
+
+/****************************/
+/*                          */
+/*     Global variables     */
+/*                          */
+/****************************/
+
+// This contains all of the precalculated parity values for a nibble (4 bits).
+static const byte _hammingCalculateParityLowNibble[] PROGMEM =
+{ 0,  3,  5,  6,  6,  5,  3,  0,  7,  4,  2,  1,  1,  2,  4,  7 };
+
+static const byte _hammingCalculateParityHighNibble[] PROGMEM =
+{ 0,  9, 10,  3, 11,  2,  1,  8, 12,  5,  6, 15,  7, 14, 13,  4 };
+
+
+/****************************/
+/*                          */
+/*      Public  methods     */
+/*                          */
+/****************************/
+
+// Given a byte to transmit, this returns the parity as a nibble
+nibble HammingCalculateParity128(byte value)
+{
+	return pgm_read_byte(&(_hammingCalculateParityLowNibble[value&0x0F])) ^ pgm_read_byte(&(_hammingCalculateParityHighNibble[value >> 4]));
+}
+
+// Given two bytes to transmit, this returns the parity
+// as a byte with the lower nibble being for the first byte,
+// and the upper nibble being for the second byte.
+byte HammingCalculateParity2416(byte first, byte second)
+{
+	return HammingCalculateParity128(second) << 4 | HammingCalculateParity128(first);
+}
diff --git a/src/Hamming/HammingCalculateParityTextbook.c b/src/Hamming/HammingCalculateParityTextbook.c
new file mode 100644
index 0000000..08e5cca
--- /dev/null
+++ b/src/Hamming/HammingCalculateParityTextbook.c
@@ -0,0 +1,100 @@
+/*
+Hamming Error-Correcting Code (ECC)
+Optimized for avr-gcc 4.8.1 in Atmel AVR Studio 6.2
+August 12, 2014
+
+You should include Hamming.c, Hamming.h, and only one of the other Hamming files in your project.
+The other Hamming files implement the same methods in different ways, that may be better or worse for your needs.
+
+This was created for LoFi in the TheHackadayPrize contest.
+http://hackaday.io/project/1552-LoFi
+
+Copyright 2014 David Cook
+RobotRoom.com
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+#include "Hamming.h"
+
+// This performs poorly on a processor that can't do multiple shifts in one instruction
+#define BitToBool(byte, n) ((byte>>(n-1)) & 1)
+
+// This is a private method that calculates half the parity
+// while shifting over any previously calculated parity for another byte.
+// This was designed for processors that cannot shift more than one bit place at a time
+nibble HammingCalculateParity2416Half(byte value, byte paritySoFar)
+{
+	// Calculate the most significant bit
+	paritySoFar |= BitToBool(value, 5) ^ BitToBool(value, 6) ^ BitToBool(value, 7) ^ BitToBool(value, 8);
+	// Shift it over
+	paritySoFar <<= 1;
+
+	// Calculate the next most significant bit
+	paritySoFar |= BitToBool(value, 2) ^ BitToBool(value, 3) ^ BitToBool(value, 4) ^ BitToBool(value, 8);
+	// Shift it over, as well as the previously calculated bit
+	paritySoFar <<= 1;
+
+	// Calculate the next most significant bit
+	paritySoFar |= BitToBool(value, 1) ^ BitToBool(value, 3) ^ BitToBool(value, 4) ^ BitToBool(value, 6) ^ BitToBool(value, 7);
+	// Shift it over, as well as the previously calculated bits
+	paritySoFar <<= 1;
+
+	// Calculate the least significant bit
+	paritySoFar |= BitToBool(value, 1) ^ BitToBool(value, 2) ^ BitToBool(value, 4) ^ BitToBool(value, 5) ^ BitToBool(value, 7);
+
+	return paritySoFar;
+}
+
+// Given a byte to transmit, this returns the parity as a nibble
+nibble HammingCalculateParity128(byte value)
+{
+	return HammingCalculateParity2416Half(value, 0);
+}
+
+// If your processor can shift multiple bit places in a single instruction, then set this to 1.
+// It will be twice as fast.
+// If your processor cannot, then set this to 0, otherwise it will be slow and large.
+#define CPU_HAS_MULTIPLE_SHIFT_INSTRUCTION 0
+
+#if CPU_HAS_MULTIPLE_SHIFT_INSTRUCTION
+// Given two bytes to transmit, this returns the parity
+// as a byte with the lower nibble being for the first byte,
+// and the upper nibble being for the second byte.
+byte HammingCalculateParity2416(byte first, byte second)
+{
+	// This is the textbook way to calculate hamming parity.
+	return	((BitToBool(first, 1) ^ BitToBool(first, 2) ^ BitToBool(first, 4) ^ BitToBool(first, 5) ^ BitToBool(first, 7))) +
+			((BitToBool(first, 1) ^ BitToBool(first, 3) ^ BitToBool(first, 4) ^ BitToBool(first, 6) ^ BitToBool(first, 7))<<1) +
+			((BitToBool(first, 2) ^ BitToBool(first, 3) ^ BitToBool(first, 4) ^ BitToBool(first, 8))<<2) +
+			((BitToBool(first, 5) ^ BitToBool(first, 6) ^ BitToBool(first, 7) ^ BitToBool(first, 8))<<3) +
+
+			((BitToBool(second, 1) ^ BitToBool(second, 2) ^ BitToBool(second, 4) ^ BitToBool(second, 5) ^ BitToBool(second, 7))<<4) +
+			((BitToBool(second, 1) ^ BitToBool(second, 3) ^ BitToBool(second, 4) ^ BitToBool(second, 6) ^ BitToBool(second, 7))<<5) +
+			((BitToBool(second, 2) ^ BitToBool(second, 3) ^ BitToBool(second, 4) ^ BitToBool(second, 8))<<6) +
+			((BitToBool(second, 5) ^ BitToBool(second, 6) ^ BitToBool(second, 7) ^ BitToBool(second, 8))<<7);
+}
+#else
+// Given two bytes to transmit, this returns the parity
+// as a byte with the lower nibble being for the first byte,
+// and the upper nibble being for the second byte.
+byte HammingCalculateParity2416(byte first, byte second)
+{
+	// This makes two calls, one for each byte.
+	// It passes the result of the second byte into the calculation for the first
+	// such that the four shift instructions and the 'or' instruction are free.
+	return HammingCalculateParity2416Half(first, HammingCalculateParity2416Half(second, 0) << 1);
+}
+#endif
+
+
diff --git a/src/Hamming/LICENSE b/src/Hamming/LICENSE
new file mode 100644
index 0000000..5c304d1
--- /dev/null
+++ b/src/Hamming/LICENSE
@@ -0,0 +1,201 @@
+Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
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diff --git a/src/Hamming/README.md b/src/Hamming/README.md
new file mode 100644
index 0000000..b6b8269
--- /dev/null
+++ b/src/Hamming/README.md
@@ -0,0 +1,4 @@
+Hamming
+=======
+
+Hamming(12,8) and (24,16) error-correcting code (ECC) in avr-gcc