Information on Result #701251
Linear OA(542, 71, F5, 20) (dual of [71, 29, 21]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,11,12,37,47}), C2 = C([0,16]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,11,12,16,37,47}) based on
- linear OA(537, 62, F5, 19) (dual of [62, 25, 20]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,37,47}, and minimum distance d ≥ |{−3,−2,…,15}|+1 = 20 (BCH-bound) [i]
- linear OA(534, 62, F5, 17) (dual of [62, 28, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(540, 62, F5, 20) (dual of [62, 22, 21]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,16,37,47}, and minimum distance d ≥ |{−3,−2,…,16}|+1 = 21 (BCH-bound) [i]
- linear OA(531, 62, F5, 16) (dual of [62, 31, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 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.