Information on Result #683338
Linear OA(5142, 640, F5, 43) (dual of [640, 498, 44]-code), using construction XX applied to C([0,21]) ⊂ C([0,20]) ⊂ C([0,18]) based on
- linear OA(5137, 626, F5, 43) (dual of [626, 489, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(5129, 626, F5, 41) (dual of [626, 497, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(5121, 626, F5, 37) (dual of [626, 505, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(51, 10, F5, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(53, 4, F5, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,5) or 4-cap in PG(2,5)), using
- dual of repetition code with length 4 [i]
Mode: Constructive and linear.
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.