A reversible code over GF(q)

An (n, k) linear code C of length n over GF(q) = Fq, a Galios field of order q, where q is a prime, is a fc-dimensional linear subspace of F"q, where F"q denotes the space of all n-tuples over GF(q). A generator matrix G of this code is a k x n matrix whose rows form a basis of C. The parity-check matrix H of this code is an(n — fc) x n matrix such that Hv = 0 for all vectors veC. The row space of (n k) x n matrix H is an (n, n — fc) linear code C called dual code of C. The Hamming weight of a vector is the number of non-zero elements in it. A code word in C consists of some fc symbols as message or information symbols and the remaining symbols as check-digits [2]. A class of codes called 'reversible codes' introduced by Massey [3] is defined as follows: