Information on Result #684356
Linear OA(523, 31, F5, 15) (dual of [31, 8, 16]-code), using construction XX applied to C([0,71]) ⊂ C([0,51]) ⊂ C([0,47]) based on
- linear OA(521, 24, F5, 18) (dual of [24, 3, 19]-code), using contraction [i] based on linear OA(593, 96, F5, 75) (dual of [96, 3, 76]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,71], and minimum distance d ≥ |{−3,−2,…,71}|+1 = 76 (BCH-bound) [i]
- linear OA(517, 24, F5, 13) (dual of [24, 7, 14]-code), using contraction [i] based on linear OA(589, 96, F5, 55) (dual of [96, 7, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,51], and minimum distance d ≥ |{−3,−2,…,51}|+1 = 56 (BCH-bound) [i]
- linear OA(516, 24, F5, 12) (dual of [24, 8, 13]-code), using contraction [i] based on linear OA(588, 96, F5, 51) (dual of [96, 8, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,47], and minimum distance d ≥ |{−3,−2,…,47}|+1 = 52 (BCH-bound) [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 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(50, 1, F5, 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.