Information on Result #813405
Linear OOA(356, 66, F3, 2, 18) (dual of [(66, 2), 76, 19]-NRT-code), using OOA 2-folding based on linear OA(356, 132, F3, 18) (dual of [132, 76, 19]-code), using
- 1 times truncation [i] based on linear OA(357, 133, F3, 19) (dual of [133, 76, 20]-code), using
- construction XX applied to C1 = C({1,8,10,13,16,19,22,25,26,31}), C2 = C({1,7,8,10,13,16,19,22,25,26}), C3 = C1 + C2 = C({1,8,10,13,16,19,22,25,26}), and C∩ = C1 ∩ C2 = C({1,7,8,10,13,16,19,22,25,26,31}) [i] based on
- 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 = {1,8,10,13,16,19,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,48}|+1 = 18 (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 = {1,7,8,10,13,16,19,22,25,26}, and minimum distance d ≥ |{10,30,50,…,−33}|+1 = 18 (BCH-bound) [i]
- linear OA(355, 121, F3, 19) (dual of [121, 66, 20]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,7,8,10,13,16,19,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,−33}|+1 = 20 (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 = {1,8,10,13,16,19,22,25,26}, and minimum distance d ≥ |{10,30,50,…,48}|+1 = 16 (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(31, 6, F3, 1) (dual of [6, 5, 2]-code) (see above)
- construction XX applied to C1 = C({1,8,10,13,16,19,22,25,26,31}), C2 = C({1,7,8,10,13,16,19,22,25,26}), C3 = C1 + C2 = C({1,8,10,13,16,19,22,25,26}), and C∩ = C1 ∩ C2 = C({1,7,8,10,13,16,19,22,25,26,31}) [i] based on
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.
Other Results with Identical Parameters
None.
Depending Results
None.