Information on Result #1738390
Digital (16, 27, 427)-net over F27, using net defined by OOA based on linear OOA(2727, 427, F27, 14, 11) (dual of [(427, 14), 5951, 12]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2727, 1282, F27, 2, 11) (dual of [(1282, 2), 2537, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2727, 1284, F27, 2, 11) (dual of [(1284, 2), 2541, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2727, 1284, F27, 11) (dual of [1284, 1257, 12]-code), using
- 546 step Varšamov–Edel lengthening with (ri) = (2, 1, 8 times 0, 1, 45 times 0, 1, 160 times 0, 1, 328 times 0) [i] based on linear OA(2721, 732, F27, 11) (dual of [732, 711, 12]-code), using
- construction XX applied to C1 = C([727,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([727,9]) [i] based on
- linear OA(2719, 728, F27, 10) (dual of [728, 709, 11]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2719, 728, F27, 10) (dual of [728, 709, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2717, 728, F27, 9) (dual of [728, 711, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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([727,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([727,9]) [i] based on
- 546 step Varšamov–Edel lengthening with (ri) = (2, 1, 8 times 0, 1, 45 times 0, 1, 160 times 0, 1, 328 times 0) [i] based on linear OA(2721, 732, F27, 11) (dual of [732, 711, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2727, 1284, F27, 11) (dual of [1284, 1257, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(2727, 1284, F27, 2, 11) (dual of [(1284, 2), 2541, 12]-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.