Information on Result #1738512
Digital (20, 33, 587)-net over F27, using net defined by OOA based on linear OOA(2733, 587, F27, 14, 13) (dual of [(587, 14), 8185, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2733, 1762, F27, 2, 13) (dual of [(1762, 2), 3491, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2733, 1763, F27, 2, 13) (dual of [(1763, 2), 3493, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2733, 1763, F27, 13) (dual of [1763, 1730, 14]-code), using
- 1023 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 24 times 0, 1, 82 times 0, 1, 187 times 0, 1, 303 times 0, 1, 417 times 0) [i] based on linear OA(2725, 732, F27, 13) (dual of [732, 707, 14]-code), using
- construction XX applied to C1 = C([727,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([727,11]) [i] based on
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [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(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(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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([727,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([727,11]) [i] based on
- 1023 step Varšamov–Edel lengthening with (ri) = (3, 4 times 0, 1, 24 times 0, 1, 82 times 0, 1, 187 times 0, 1, 303 times 0, 1, 417 times 0) [i] based on linear OA(2725, 732, F27, 13) (dual of [732, 707, 14]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2733, 1763, F27, 13) (dual of [1763, 1730, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(2733, 1763, F27, 2, 13) (dual of [(1763, 2), 3493, 14]-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.