Information on Result #1821980
OA(27106, 19772, S27, 30), using (u, u+v)-construction based on
- OA(2720, 82, S27, 15), using
- discarding parts of the base [i] based on linear OA(8115, 82, F81, 15) (dual of [82, 67, 16]-code or 82-arc in PG(14,81)), using
- extended Reed–Solomon code RSe(67,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(8115, 82, F81, 15) (dual of [82, 67, 16]-code or 82-arc in PG(14,81)), using
- linear OA(2786, 19690, F27, 30) (dual of [19690, 19604, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
Mode: Constructive.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.