Information on Result #1730472
Digital (133, 172, 4457)-net over F8, using net defined by OOA based on linear OOA(8172, 4457, F8, 45, 39) (dual of [(4457, 45), 200393, 40]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OOA(8172, 31200, F8, 3, 39) (dual of [(31200, 3), 93428, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8172, 31206, F8, 3, 39) (dual of [(31206, 3), 93446, 40]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8172, 31206, F8, 39) (dual of [31206, 31034, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(8172, 32780, F8, 39) (dual of [32780, 32608, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(8171, 32769, F8, 39) (dual of [32769, 32598, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(8161, 32769, F8, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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 C([0,19]) ⊂ C([0,18]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8172, 32780, F8, 39) (dual of [32780, 32608, 40]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8172, 31206, F8, 39) (dual of [31206, 31034, 40]-code), using
- discarding factors / shortening the dual code based on linear OOA(8172, 31206, F8, 3, 39) (dual of [(31206, 3), 93446, 40]-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.