Question

4. Let C be the code consisting of the solutions to the matrix equation Ax = 0, where 0 1 1 1 O 0 1 1 1 0 1 1 1 0 0 0 1 A = 1 Determine the codewords of C, and determine the distance and error cor- rection capability of C

Answer 1

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each Low vechor and A to MulApy Step 3 lode word riotton 0IIIO! 1 1 1 0 0 0 = 0+0+0, 0+0+0,0+0+0, 0+0+0,0+0+0, Coo0000) O+041,0+0+1,0+0+0, 0+0+0,0+0+0 Cadeuad 1 2x A Codeuoord 2 0-+0+0, 00, 0+1+0, 0t1+0,0+0+0,0+ Codewond 3 x A O*140 Co4041, Ryx A 041 0ttt, 01+0, 0+0+0, 0+ Adutitin in Modulo 2 Codewsd 4 Dolool] 1t0+0, 0+0+0, 1to+0, +0t0, l+0+0, 0+0t0) RxA [ιoιιd Codewsel s +0+t,0t0+1, t o+1, lt0+0, 1t0t0, ot0t0) Adcitan in Rox A Co10110] Codeword 6 Modulo 2 [ttoto, 01+0, it+D, t1+0, It0+0, 0+to) Additon in 1o011 Codeword - Madulo 2 +0+, 0t1tl, +1+l, ti+o, +0+0, 0t1to) ALlihon -Toolol1] Codeword 8 Modulo 2. In C 000000, 111000o, 011o1, lool01, l0111o,0l01to, Itool The nallert -2evo odewod 3 arac dhistance 00000 0 t1oo0 t can detect up to 2 evros (d-) eros and iorrect upto (d-) errod - 1