Information on Result #731775
Linear OA(7110, 117, F7, 82) (dual of [117, 7, 83]-code), using juxtaposition based on
- linear OA(750, 57, F7, 40) (dual of [57, 7, 41]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,29], and minimum distance d ≥ |{−10,−9,…,29}|+1 = 41 (BCH-bound) [i]
- linear OA(753, 60, F7, 41) (dual of [60, 7, 42]-code), using
- construction X applied to C([0,80]) ⊂ C([0,78]) [i] based on
- linear OA(753, 57, F7, 41) (dual of [57, 4, 42]-code), using contraction [i] based on linear OA(7110, 114, F7, 83) (dual of [114, 4, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,80], and minimum distance d ≥ |{−2,−1,…,80}|+1 = 84 (BCH-bound) [i]
- linear OA(750, 57, F7, 40) (dual of [57, 7, 41]-code), using contraction [i] based on linear OA(7107, 114, F7, 81) (dual of [114, 7, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 114 | 73−1, defining interval I = [0,78], and minimum distance d ≥ |{−2,−1,…,78}|+1 = 82 (BCH-bound) [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C([0,80]) ⊂ C([0,78]) [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.
Other Results with Identical Parameters
None.
Depending Results
None.