Information on Result #1738572
Digital (19, 33, 242)-net over F27, using net defined by OOA based on linear OOA(2733, 242, F27, 18, 14) (dual of [(242, 18), 4323, 15]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(2733, 969, F27, 2, 14) (dual of [(969, 2), 1905, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2733, 971, F27, 2, 14) (dual of [(971, 2), 1909, 15]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2733, 971, F27, 14) (dual of [971, 938, 15]-code), using
- 233 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 20 times 0, 1, 61 times 0, 1, 144 times 0) [i] based on linear OA(2727, 732, F27, 14) (dual of [732, 705, 15]-code), using
- construction XX applied to C1 = C([727,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([727,12]) [i] based on
- linear OA(2725, 728, F27, 13) (dual of [728, 703, 14]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2725, 728, F27, 13) (dual of [728, 703, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2727, 728, F27, 14) (dual of [728, 701, 15]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [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([727,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([727,12]) [i] based on
- 233 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 20 times 0, 1, 61 times 0, 1, 144 times 0) [i] based on linear OA(2727, 732, F27, 14) (dual of [732, 705, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2733, 971, F27, 14) (dual of [971, 938, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(2733, 971, F27, 2, 14) (dual of [(971, 2), 1909, 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.