Information on Result #1725390
Digital (43, 57, 1688)-net over F7, using net defined by OOA based on linear OOA(757, 1688, F7, 21, 14) (dual of [(1688, 21), 35391, 15]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(757, 5065, F7, 3, 14) (dual of [(5065, 3), 15138, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(757, 5066, F7, 3, 14) (dual of [(5066, 3), 15141, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(757, 5066, F7, 14) (dual of [5066, 5009, 15]-code), using
- 257 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 40 times 0, 1, 209 times 0) [i] based on linear OA(754, 4806, F7, 14) (dual of [4806, 4752, 15]-code), using
- trace code [i] based on linear OA(4927, 2403, F49, 14) (dual of [2403, 2376, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(4927, 2401, F49, 14) (dual of [2401, 2374, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(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(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(4927, 2403, F49, 14) (dual of [2403, 2376, 15]-code), using
- 257 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 40 times 0, 1, 209 times 0) [i] based on linear OA(754, 4806, F7, 14) (dual of [4806, 4752, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(757, 5066, F7, 14) (dual of [5066, 5009, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(757, 5066, F7, 3, 14) (dual of [(5066, 3), 15141, 15]-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.