Information on Result #685860
Linear OA(762, 77, F7, 38) (dual of [77, 15, 39]-code), using construction XX applied to C([0,79]) ⊂ C([0,49]) ⊂ C([0,47]) based on
- linear OA(745, 48, F7, 40) (dual of [48, 3, 41]-code), using contraction [i] based on linear OA(793, 96, F7, 81) (dual of [96, 3, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using contraction [i] based on linear OA(782, 96, F7, 51) (dual of [96, 14, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,49], and minimum distance d ≥ |{−1,0,…,49}|+1 = 52 (BCH-bound) [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using contraction [i] based on linear OA(781, 96, F7, 49) (dual of [96, 15, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,47], and minimum distance d ≥ |{−1,0,…,47}|+1 = 50 (BCH-bound) [i]
- linear OA(716, 28, F7, 12) (dual of [28, 12, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-code), using
- extended quadratic residue code Qe(32,7) [i]
- discarding factors / shortening the dual code based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-code), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.