Information on Result #1724008
Digital (77, 103, 454)-net over F5, using net defined by OOA based on linear OOA(5103, 454, F5, 33, 26) (dual of [(454, 33), 14879, 27]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(5103, 2271, F5, 3, 26) (dual of [(2271, 3), 6710, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5103, 2274, F5, 3, 26) (dual of [(2274, 3), 6719, 27]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5103, 2274, F5, 26) (dual of [2274, 2171, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5103, 3133, F5, 26) (dual of [3133, 3030, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(596, 3125, F5, 24) (dual of [3125, 3029, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(591, 3125, F5, 23) (dual of [3125, 3034, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(51, 7, F5, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(5103, 3133, F5, 26) (dual of [3133, 3030, 27]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5103, 2274, F5, 26) (dual of [2274, 2171, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(5103, 2274, F5, 3, 26) (dual of [(2274, 3), 6719, 27]-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.