Information on Result #677628
Linear OA(387, 96, F3, 53) (dual of [96, 9, 54]-code), using construction XX applied to C1 = C([0,87]), C2 = C([1,105]), C3 = C1 + C2 = C([1,87]), and C∩ = C1 ∩ C2 = C([0,105]) based on
- linear OA(370, 80, F3, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3150, 160, F3, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (BCH-bound) [i]
- linear OA(375, 80, F3, 52) (dual of [80, 5, 53]-code), using contraction [i] based on linear OA(3155, 160, F3, 105) (dual of [160, 5, 106]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,105], and designed minimum distance d ≥ |I|+1 = 106 [i]
- linear OA(376, 80, F3, 53) (dual of [80, 4, 54]-code), using contraction [i] based on linear OA(3156, 160, F3, 107) (dual of [160, 4, 108]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,105], and minimum distance d ≥ |{−5,8,21,…,−67}|+1 = 108 (BCH-bound) [i]
- linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using contraction [i] based on linear OA(3149, 160, F3, 87) (dual of [160, 11, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(311, 15, F3, 8) (dual of [15, 4, 9]-code), using
- construction X applied to C([0,6]) ⊂ C([1,6]) [i] based on
- linear OA(310, 13, F3, 8) (dual of [13, 3, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [0,6], and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(39, 13, F3, 6) (dual of [13, 4, 7]-code), using the narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([1,6]) [i] based on
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.