Information on Result #1831784
OOA(27110, 4197584, S27, 2, 18), using (u, u+v)-construction based on
- OOA(2724, 3283, S27, 2, 9), using
- OOA 2-folding [i] based on OA(2724, 6566, S27, 9), using
- discarding factors based on OA(2724, 6567, S27, 9), using
- discarding parts of the base [i] based on linear OA(8118, 6567, F81, 9) (dual of [6567, 6549, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(8117, 6562, F81, 9) (dual of [6562, 6545, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- discarding parts of the base [i] based on linear OA(8118, 6567, F81, 9) (dual of [6567, 6549, 10]-code), using
- discarding factors based on OA(2724, 6567, S27, 9), using
- OOA 2-folding [i] based on OA(2724, 6566, S27, 9), using
- linear OOA(2786, 4194301, F27, 2, 18) (dual of [(4194301, 2), 8388516, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2786, 8388602, F27, 18) (dual of [8388602, 8388516, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- OOA 2-folding [i] based on linear OA(2786, 8388602, F27, 18) (dual of [8388602, 8388516, 19]-code), using
Mode: Constructive.
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.