CODES EQUIVALENCES BY A GRAY MAP - (NIM: 20114042), DEFITA
Two linear codes possibly have same error-correcting capability if there is a linear map between them which is distance preserving, it's called isometry. Every monomial map is an isometry but the converse is not always true. MacWilliams Equivalence Theorem states that two codes over fields are Hamming weight isometry if and only if they are monomial equivalent. Two codes are monomial equivalent if there is a monomial map between them. Wood generalized the equivalence theorem by considering weights other than Hamming weight, that is Lee weight. Wood proved that the Lee weight satisfy the equivalence theorem for the ring ZN for N is on the form 2p + 1, where N and p are both primes. Aleams Barra also proved that the Lee weight satisfy the equivalence theorem for the ring ZN for N is on the form 4p+1, where N and p are both primes. Beside that, Wood claimed that the Lee weight satisfy the equivalence theorem for the ring ZN for N is on the form 2k and 3k for a positive integer k. In this thesis, will be identified Wood's result, that is equivalence theorem for the Lee weight for the ring Z2k with a Gray map from Z2k to Z2k1 2 .