Information on Result #701184
Linear OA(524, 36, F5, 14) (dual of [36, 12, 15]-code), using construction XX applied to C1 = C({1,2,6,7,8,9,12,13}), C2 = C([0,12]), C3 = C1 + C2 = C({1,2,6,7,8,9,12}), and C∩ = C1 ∩ C2 = C([0,13]) based on
- linear OA(514, 24, F5, 9) (dual of [24, 10, 10]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {1,2,6,7,8,9,12,13}, and minimum distance d ≥ |{5,6,…,13}|+1 = 10 (BCH-bound) [i]
- linear OA(517, 24, F5, 13) (dual of [24, 7, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(519, 24, F5, 14) (dual of [24, 5, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(512, 24, F5, 8) (dual of [24, 12, 9]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {1,2,6,7,8,9,12}, and minimum distance d ≥ |{5,6,…,12}|+1 = 9 (BCH-bound) [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
- linear OA(55, 10, F5, 4) (dual of [10, 5, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(55, 12, F5, 4) (dual of [12, 7, 5]-code), 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.