Information on Result #1738886
Digital (25, 43, 232)-net over F27, using net defined by OOA based on linear OOA(2743, 232, F27, 22, 18) (dual of [(232, 22), 5061, 19]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(2743, 1161, F27, 2, 18) (dual of [(1161, 2), 2279, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2743, 1162, F27, 2, 18) (dual of [(1162, 2), 2281, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2743, 1162, F27, 18) (dual of [1162, 1119, 19]-code), using
- 422 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 7 times 0, 1, 24 times 0, 1, 63 times 0, 1, 128 times 0, 1, 192 times 0) [i] based on linear OA(2735, 732, F27, 18) (dual of [732, 697, 19]-code), using
- construction XX applied to C1 = C([727,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([727,16]) [i] based on
- linear OA(2733, 728, F27, 17) (dual of [728, 695, 18]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2733, 728, F27, 17) (dual of [728, 695, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2735, 728, F27, 18) (dual of [728, 693, 19]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2731, 728, F27, 16) (dual of [728, 697, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [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([727,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([727,16]) [i] based on
- 422 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 7 times 0, 1, 24 times 0, 1, 63 times 0, 1, 128 times 0, 1, 192 times 0) [i] based on linear OA(2735, 732, F27, 18) (dual of [732, 697, 19]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2743, 1162, F27, 18) (dual of [1162, 1119, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(2743, 1162, F27, 2, 18) (dual of [(1162, 2), 2281, 19]-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.