Information on Result #1727004
Digital (42, 51, 681447)-net over F8, using net defined by OOA based on linear OOA(851, 681447, F8, 10, 9) (dual of [(681447, 10), 6814419, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(851, 1362895, F8, 2, 9) (dual of [(1362895, 2), 2725739, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(851, 1362895, F8, 9) (dual of [1362895, 1362844, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(851, 2097160, F8, 9) (dual of [2097160, 2097109, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(843, 2097152, F8, 7) (dual of [2097152, 2097109, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(851, 2097160, F8, 9) (dual of [2097160, 2097109, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(851, 1362895, F8, 9) (dual of [1362895, 1362844, 10]-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.