Information on Result #1070351
Linear OOA(12878, 2621441, F128, 4, 15) (dual of [(2621441, 4), 10485686, 16]-NRT-code), using OOA 2-folding based on linear OOA(12878, 5242882, F128, 2, 15) (dual of [(5242882, 2), 10485686, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12821, 1048581, F128, 2, 7) (dual of [(1048581, 2), 2097141, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12821, 2097162, F128, 7) (dual of [2097162, 2097141, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(12821, 2097163, F128, 7) (dual of [2097163, 2097142, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(12821, 2097163, F128, 7) (dual of [2097163, 2097142, 8]-code), using
- OOA 2-folding [i] based on linear OA(12821, 2097162, F128, 7) (dual of [2097162, 2097141, 8]-code), using
- linear OOA(12857, 4194301, F128, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12857, 8388602, F128, 15) (dual of [8388602, 8388545, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(12857, large, F128, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12857, large, F128, 15) (dual of [large, large−57, 16]-code), using
- OOA 2-folding [i] based on linear OA(12857, 8388602, F128, 15) (dual of [8388602, 8388545, 16]-code), using
- linear OOA(12821, 1048581, F128, 2, 7) (dual of [(1048581, 2), 2097141, 8]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.