Information on Result #701162
Linear OA(515, 33, F5, 8) (dual of [33, 18, 9]-code), using construction XX applied to C1 = C({1,3,4,6,7}), C2 = C([0,4]), C3 = C1 + C2 = C({1,3,4}), and C∩ = C1 ∩ C2 = C([0,7]) based on
- linear OA(59, 24, F5, 5) (dual of [24, 15, 6]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {1,3,4,6,7}, and minimum distance d ≥ |{3,4,5,6,7}|+1 = 6 (BCH-bound) [i]
- linear OA(59, 24, F5, 6) (dual of [24, 15, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(512, 24, F5, 8) (dual of [24, 12, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(56, 24, F5, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,5)), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {1,3,4}, and minimum distance d ≥ |{3,4,5}|+1 = 4 (BCH-bound) [i]
- linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-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.