Information on Result #1736686
Digital (54, 72, 78128)-net over F25, using net defined by OOA based on linear OOA(2572, 78128, F25, 22, 18) (dual of [(78128, 22), 1718744, 19]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(2572, 390641, F25, 2, 18) (dual of [(390641, 2), 781210, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2572, 390644, F25, 2, 18) (dual of [(390644, 2), 781216, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2572, 390644, F25, 18) (dual of [390644, 390572, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(2569, 390625, F25, 18) (dual of [390625, 390556, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2572, 390644, F25, 18) (dual of [390644, 390572, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(2572, 390644, F25, 2, 18) (dual of [(390644, 2), 781216, 19]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.