Information on Result #701190
Linear OA(531, 39, F5, 20) (dual of [39, 8, 21]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,14,19}), C2 = C([0,13]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,12,13,14,19}) based on
- linear OA(520, 24, F5, 17) (dual of [24, 4, 18]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,4,6,7,8,9,14,19}, and minimum distance d ≥ |{−5,−4,…,11}|+1 = 18 (BCH-bound) [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(523, 24, F5, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,5)), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,4,6,7,8,9,12,13,14,19}, and minimum distance d ≥ |{1,8,15,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(516, 24, F5, 12) (dual of [24, 8, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(56, 10, F5, 5) (dual of [10, 4, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(56, 12, F5, 5) (dual of [12, 6, 6]-code), using
- extended quadratic residue code Qe(12,5) [i]
- discarding factors / shortening the dual code based on linear OA(56, 12, F5, 5) (dual of [12, 6, 6]-code), using
- linear OA(52, 5, F5, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
- Reed–Solomon code RS(3,5) [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.