Information on Result #1806612
Digital (36, 67, 799)-net over F27, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(2767, 799, F27, 31) (dual of [799, 732, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2767, 800, F27, 31) (dual of [800, 733, 32]-code), using
- 59 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 15 times 0, 1, 28 times 0) [i] based on linear OA(2758, 732, F27, 31) (dual of [732, 674, 32]-code), using
- construction XX applied to C1 = C([727,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([727,29]) [i] based on
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2758, 728, F27, 31) (dual of [728, 670, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2754, 728, F27, 29) (dual of [728, 674, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [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([727,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([727,29]) [i] based on
- 59 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 15 times 0, 1, 28 times 0) [i] based on linear OA(2758, 732, F27, 31) (dual of [732, 674, 32]-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.