Information on Result #689652
Linear OA(978, 6576, F9, 21) (dual of [6576, 6498, 22]-code), using construction XX applied to C([0,10]) ⊂ C([0,9]) ⊂ C([0,7]) based on
- linear OA(973, 6562, F9, 21) (dual of [6562, 6489, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(965, 6562, F9, 19) (dual of [6562, 6497, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(957, 6562, F9, 15) (dual of [6562, 6505, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(91, 10, F9, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(93, 4, F9, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,9) or 4-cap in PG(2,9)), 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.