Information on Result #701144
Linear OA(428, 94, F4, 10) (dual of [94, 66, 11]-code), using construction XX applied to C1 = C({5,7,9,13,34,37}), C2 = C({5,6,7,9,13}), C3 = C1 + C2 = C({5,7,9,13}), and C∩ = C1 ∩ C2 = C({5,6,7,9,13,34,37}) based on
- linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {5,7,9,13,34,37}, and minimum distance d ≥ |{38,52,66,…,−20}|+1 = 10 (BCH-bound) [i]
- linear OA(420, 85, F4, 7) (dual of [85, 65, 8]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {5,6,7,9,13}, and minimum distance d ≥ |{24,38,52,…,23}|+1 = 8 (BCH-bound) [i]
- linear OA(426, 85, F4, 10) (dual of [85, 59, 11]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {5,6,7,9,13,34,37}, and minimum distance d ≥ |{24,38,52,…,−20}|+1 = 11 (BCH-bound) [i]
- linear OA(416, 85, F4, 6) (dual of [85, 69, 7]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {5,7,9,13}, and minimum distance d ≥ |{38,52,66,…,23}|+1 = 7 (BCH-bound) [i]
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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.