Information on Result #1725274
Digital (40, 53, 2535)-net over F7, using net defined by OOA based on linear OOA(753, 2535, F7, 15, 13) (dual of [(2535, 15), 37972, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(753, 5071, F7, 3, 13) (dual of [(5071, 3), 15160, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(753, 5072, F7, 3, 13) (dual of [(5072, 3), 15163, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(753, 5072, F7, 13) (dual of [5072, 5019, 14]-code), using
- 263 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 40 times 0, 1, 215 times 0) [i] based on linear OA(750, 4806, F7, 13) (dual of [4806, 4756, 14]-code), using
- trace code [i] based on linear OA(4925, 2403, F49, 13) (dual of [2403, 2378, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- trace code [i] based on linear OA(4925, 2403, F49, 13) (dual of [2403, 2378, 14]-code), using
- 263 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 40 times 0, 1, 215 times 0) [i] based on linear OA(750, 4806, F7, 13) (dual of [4806, 4756, 14]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(753, 5072, F7, 13) (dual of [5072, 5019, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(753, 5072, F7, 3, 13) (dual of [(5072, 3), 15163, 14]-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.