Information on Result #700908
Linear OA(354, 135, F3, 17) (dual of [135, 81, 18]-code), using construction XX applied to C1 = C({1,5,7,11,13,16,17,19,40}), C2 = C({1,5,7,11,13,16,17,19,25}), C3 = C1 + C2 = C({1,5,7,11,13,16,17,19}), and C∩ = C1 ∩ C2 = C({1,5,7,11,13,16,17,19,25,40}) based on
- linear OA(345, 121, F3, 14) (dual of [121, 76, 15]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,5,7,11,13,16,17,19,40}, and minimum distance d ≥ |{−3,−1,1,…,23}|+1 = 15 (BCH-bound) [i]
- linear OA(345, 121, F3, 15) (dual of [121, 76, 16]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,5,7,11,13,16,17,19,25}, and minimum distance d ≥ |{1,3,5,…,29}|+1 = 16 (BCH-bound) [i]
- linear OA(350, 121, F3, 17) (dual of [121, 71, 18]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,5,7,11,13,16,17,19,25,40}, and minimum distance d ≥ |{−3,−1,1,…,29}|+1 = 18 (BCH-bound) [i]
- linear OA(340, 121, F3, 12) (dual of [121, 81, 13]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,5,7,11,13,16,17,19}, and minimum distance d ≥ |{1,3,5,…,23}|+1 = 13 (BCH-bound) [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(33, 8, F3, 2) (dual of [8, 5, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), 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.