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# Hamming code in C

## Hamming code

## Hamming Code Algorithm

In telecommunication, a **Hamming code** is a linearerror-correcting code named after its inventor, Richard Hamming. Hamming codes can detect up to two simultaneous bit errors, and correct single-bit errors; thus, reliable communication is possible when the Hamming distance between the transmitted and received bit patterns is less than or equal to one. By contrast, the simple parity code cannot correct errors, and can only detect an odd number of errors.

In mathematical terms, Hamming codes are a class of binary linear codes. For each integer there is a code with *m* parity bits and 2^{m} − *m* − 1 data bits. The parity-check matrix of a Hamming code is constructed by listing all columns of length *m* that are pairwise independent. Hamming codes are an example of perfect codes, codes that exactly match the theoretical upper bound on the number of distinct code words for a given number of bits and ability to correct errors.

Because of the simplicity of Hamming codes, they are widely used in computer memory (RAM). In particular, a single-error-correcting *and* double-error-detecting variant commonly referred to as **SECDED**.

## Hamming code in C

/* Program to find hamming code*/ #include<stdio.h> #include<stdlib.h> char data[5]; int encoded[8],edata[7],syndrome[3]; int hmatrix[3][7] = { 1,0,0,0,1,1,1, 0,1,0,1,0,1,1, 0,0,1,1,1,0,1 }; char gmatrix[4][8]={"0111000","1010100","1100010","1110001"}; int main(){ int i,j; system("clear"); printf("\nHamming code----- Encoding\n"); printf("Enter 4 bit data : "); scanf("%s",data); printf("\nGenerator matrix\n"); for(i=0;i<4;i++) printf("%s\n",gmatrix[i]); printf("\nEncoded data "); for(i=0;i<7;i++) { for(j=0;j<4;j++) encoded[i]+=((data[j]-'0')*(gmatrix[j][i]-'0')); encoded[i]=encoded[i]%2; printf("%d ",encoded[i]); } printf("\nHamming code----- Decoding\n"); printf("Enter encoded bits as recieved : "); for(i=0;i<7;i++) scanf("%d",&edata[i]); for(i=0;i<3;i++) { for(j=0;j<7;j++) syndrome[i]+=(edata[j]*hmatrix[i][j]); syndrome[i]=syndrome[i]%2; } for(j=0;j<7;j++) if((syndrome[0]==hmatrix[0][j]) && (syndrome[1]==hmatrix[1][j])&& (syndrome[2]==hmatrix[2][j])) break; if(j==7) printf("\nError free\n"); else { printf("\nError recieved at bit number %d of data\n",j+1); edata[j]=!edata[j]; printf("\nCorrect data should be : "); for(i=0;i<7;i++) printf("%d",edata[i]); } return 0; }

## Makefile

a.out:hammingCode.c gcc -ggdb hammingCode.c PHONY:clean clean: rm a.out *~

## Example output

Hamming code----- Encoding

Enter 4 bit data : 1011

Generator matrix

0111000

1010100

1100010

1110001

Encoded data 0 1 0 1 0 1 1

Hamming code----- Decoding

Enter encoded bits as received : 0 1 0 1 1 1 1

Error received at bit number 5 of data

Correct data should be : 0101011

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