Information on Result #1734696
Digital (61, 81, 22629)-net over F16, using net defined by OOA based on linear OOA(1681, 22629, F16, 22, 20) (dual of [(22629, 22), 497757, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(1681, 113146, F16, 2, 20) (dual of [(113146, 2), 226211, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1681, 113148, F16, 2, 20) (dual of [(113148, 2), 226215, 21]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1681, 113148, F16, 20) (dual of [113148, 113067, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1681, 131083, F16, 20) (dual of [131083, 131002, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1680, 131082, F16, 20) (dual of [131082, 131002, 21]-code), using
- trace code [i] based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1680, 131082, F16, 20) (dual of [131082, 131002, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1681, 131083, F16, 20) (dual of [131083, 131002, 21]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1681, 113148, F16, 20) (dual of [113148, 113067, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(1681, 113148, F16, 2, 20) (dual of [(113148, 2), 226215, 21]-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.