Information on Result #1303795
Linear OA(16113, 4114, F16, 39) (dual of [4114, 4001, 40]-code), using construction X with Varšamov bound based on
- linear OA(16112, 4112, F16, 39) (dual of [4112, 4000, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,17]) [i] based on
- linear OA(16109, 4097, F16, 39) (dual of [4097, 3988, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(1697, 4097, F16, 35) (dual of [4097, 4000, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(163, 15, F16, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- construction X applied to C([0,19]) ⊂ C([0,17]) [i] based on
- linear OA(16112, 4113, F16, 38) (dual of [4113, 4001, 39]-code), using Gilbert–Varšamov bound and bm = 16112 > Vbs−1(k−1) = 106 247318 815412 757241 067734 658419 424252 759641 839736 930409 614419 822953 623071 838236 528677 907111 657400 086258 627762 553286 459157 057974 774656 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.