Divisible Codes - A Survey
Harold N. Ward · Bulgarian Digital Mathematics Library (BulDML) at IMI-BAS (Institute of Mathematics and Informatics) · 2001
Abstract. This paper surveys parts of the study of divisibility proper-ties of codes. The survey begins with the motivating background involving polynomials over finite fields. Then it presents recent results on bounds and applications to optimal codes. 1. Introduction. Let C be an [n, k, d]q code over GF (q), where q is a power of the prime p. Following Assmus and Mattson [2], we shall construe C as a k-dimensional GF (q)-vector space endowed with an indexed set Λ = Λ(C) of n coding (or coordinate) functionals λ1,..., λn that belong to the dual vector space C∗. A member c of C is encoded as the n-tuple (λ1(c),..., λn(c)) in the ambient