On triple-sum-sets and two or three weights codes

Complete weight enumerators of two classes of linear codes

“…Proof: Note that both e/d and m/d are even. By Theorem 4.1 in [7], it is easy to see that f (X) = 0 has p 2d solutions in F q . So does the equation…”

“…Thus, weight distribution is a significant research topic in coding theory and was studied in [2], [4], [7], [8], [9], [10], [14], [30], [31]. Let F p = {0, 1, .…”

Linear Codes From Some 2-Designs

“…There is a survey on two-weight codes [6]. Some interesting two-weight and three-weight codes were presented in [5], [13], [15], [25], [32], [33], [49], and [52].…”

“…Hence, the weight distribution of C D f is given by the multiset in (15). Then by assumption, wt(c w ) > 0 for every nonzero w ∈ GF(2 m ).…”

“…It looks hard to determine the weight distribution of the code C D( ρ ) . When m = 5, the binary code C D( ρ ) in the Glynn II case has parameters [15,5,6] and the weight enumerator 1 + 10z 6 + 15z 8 + 6z 10 . When m = 7, the binary code C D( ρ ) in the Glynn II case has parameters [63, 7, 28] and the weight enumerator 1 + 36z 28 + 63z 32 + 28z 36 .…”