Information on Result #1197466
Digital (42, 51, 2102071)-net over F27, using net defined by OOA based on linear OOA(2751, 2102071, F27, 10, 9) (dual of [(2102071, 10), 21020659, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2751, 4204143, F27, 2, 9) (dual of [(4204143, 2), 8408235, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2751, 4204144, F27, 2, 9) (dual of [(4204144, 2), 8408237, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2710, 9843, F27, 2, 4) (dual of [(9843, 2), 19676, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2710, 19686, F27, 4) (dual of [19686, 19676, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2710, 19683, F27, 4) (dual of [19683, 19673, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(277, 19683, F27, 3) (dual of [19683, 19676, 4]-code or 19683-cap in PG(6,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 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
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- OOA 2-folding [i] based on linear OA(2710, 19686, F27, 4) (dual of [19686, 19676, 5]-code), using
- linear OOA(2741, 4194301, F27, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2741, 8388602, F27, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2741, large, F27, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2741, large, F27, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(2741, 8388602, F27, 9) (dual of [8388602, 8388561, 10]-code), using
- linear OOA(2710, 9843, F27, 2, 4) (dual of [(9843, 2), 19676, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2751, 4204144, F27, 2, 9) (dual of [(4204144, 2), 8408237, 10]-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.