Information on Result #1806153
Digital (24, 44, 755)-net over F27, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(2744, 755, F27, 20) (dual of [755, 711, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2744, 762, F27, 20) (dual of [762, 718, 21]-code), using
- 25 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 17 times 0) [i] based on linear OA(2739, 732, F27, 20) (dual of [732, 693, 21]-code), using
- construction XX applied to C1 = C([727,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([727,18]) [i] based on
- linear OA(2737, 728, F27, 19) (dual of [728, 691, 20]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2737, 728, F27, 19) (dual of [728, 691, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2735, 728, F27, 18) (dual of [728, 693, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([727,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([727,18]) [i] based on
- 25 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 17 times 0) [i] based on linear OA(2739, 732, F27, 20) (dual of [732, 693, 21]-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.