LINEAR CODES WITH BALANCED WEIGHT DISTRIBUTION

In this paper, we study particular linear codes defined over F-q with an astonishing property, their weight distribution is balanced, i.e. there is the same number of codewords for each nonzero weight of the code. We call these codes BWD-codes. We first study BWD-codes by means of the Pless identities and we completely characterize the two-weight projective case. We study the class of codes defined under subgroups of the multiplicative group of F-qs, using the Gauss sums. Then, given a prime p and an integer N dividing p - 1, we construct all the N-weight BWD-codes of that class. We conclude this paper by some tables of BWD-codes and an open problem.