Information on Result #684372
Linear OA(519, 27, F5, 14) (dual of [27, 8, 15]-code), using construction XX applied to C1 = C([0,51]), C2 = C([1,55]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,55]) based on
- 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(518, 24, F5, 13) (dual of [24, 6, 14]-code), using contraction [i] based on linear OA(590, 96, F5, 55) (dual of [96, 6, 56]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,55], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(519, 24, F5, 14) (dual of [24, 5, 15]-code), using contraction [i] based on linear OA(591, 96, F5, 59) (dual of [96, 5, 60]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,55], and minimum distance d ≥ |{−3,−2,…,55}|+1 = 60 (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 narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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.