Information on Result #1726948
Digital (43, 51, 1048583)-net over F8, using net defined by OOA based on linear OOA(851, 1048583, F8, 10, 8) (dual of [(1048583, 10), 10485779, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(851, 2097167, F8, 2, 8) (dual of [(2097167, 2), 4194283, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(851, 2097168, F8, 2, 8) (dual of [(2097168, 2), 4194285, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(851, 2097168, F8, 8) (dual of [2097168, 2097117, 9]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(5) [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(836, 2097152, F8, 6) (dual of [2097152, 2097116, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(815, 16, F8, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,8)), using
- dual of repetition code with length 16 [i]
- linear OA(81, 16, F8, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(851, 2097168, F8, 8) (dual of [2097168, 2097117, 9]-code), using
- discarding factors / shortening the dual code based on linear OOA(851, 2097168, F8, 2, 8) (dual of [(2097168, 2), 4194285, 9]-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.