Information on Result #701173
Linear OA(525, 38, F5, 14) (dual of [38, 13, 15]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,9,14,18,19}), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,9,14,18,19}) based on
- linear OA(517, 24, F5, 13) (dual of [24, 7, 14]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,4,6,9,14,18,19}, and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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(519, 24, F5, 14) (dual of [24, 5, 15]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,4,6,7,9,14,18,19}, and minimum distance d ≥ |{−6,−5,…,7}|+1 = 15 (BCH-bound) [i]
- linear OA(510, 24, F5, 7) (dual of [24, 14, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(56, 12, F5, 5) (dual of [12, 6, 6]-code), using
- extended quadratic residue code Qe(12,5) [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.