Information on Result #1303815
Linear OA(16119, 4114, F16, 41) (dual of [4114, 3995, 42]-code), using construction X with Varšamov bound based on
- linear OA(16118, 4112, F16, 41) (dual of [4112, 3994, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,18]) [i] based on
- linear OA(16115, 4097, F16, 41) (dual of [4097, 3982, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(16103, 4097, F16, 37) (dual of [4097, 3994, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (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([0,20]) ⊂ C([0,18]) [i] based on
- linear OA(16118, 4113, F16, 40) (dual of [4113, 3995, 41]-code), using Gilbert–Varšamov bound and bm = 16118 > Vbs−1(k−1) = 267 802904 397652 357907 111924 077336 239997 624268 819894 312398 740591 016780 691852 344640 482573 589840 735669 722075 582488 529672 381472 494313 307974 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.