Monotone Span Program vs. Linear Code

A Class of Linear Codes with Three and Five Weights

“…Then The dimension of C Da equals m, since wt(c a ) > 0. (p, m, a) = (3, 3, 1), then C D1 has parameters [9,3,4] and weight enumerator 1+6x 4 +3x 5 + 8x 6 + 6x 7 + 3x 8 , which is consistent with Theorem 1.…”

“…One of the general constructions of linear codes is based on a proper selection of a subset of finite fields, and recently many classes of (optimal) linear codes with a few weights were produced by this method (see Refs. [5][6][7][8][9] for example). Below we introduce some concepts of linear code.…”