MDS codes over finite fields

03/12/2019

∙

by   Ted Hurley, et al.

∙

0

∙

share

The mds (maximum distance separable) conjecture claims that a nontrivial linear mds [n,k] code over the finite field GF(q) satisfies n ≤ (q + 1), except when q is even and k = 3 or k = q- 1 in which case it satisfies n ≤ (q + 2). For given field GF(q) and any given k, series of mds [q+1,k] codes are constructed. Any [n,3] mds or [n,n-3] mds code over GF(q) must satisfy n≤ (q+1) for q odd and n≤ (q+2) for q even. For even q, mds [q+2,3] and mds [q+2, q-1] codes are constructed over GF(q). The codes constructed have efficient encoding and decoding algorithms.