Information on Result #700912
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}) 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)
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(358, 134, F3, 19) (dual of [134, 76, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(360, 136, F3, 19) (dual of [136, 76, 20]-code) | [i] | ||
| 3 | Linear OA(356, 132, F3, 18) (dual of [132, 76, 19]-code) | [i] | Truncation | |
| 4 | Linear OOA(357, 66, F3, 2, 19) (dual of [(66, 2), 75, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(357, 44, F3, 3, 19) (dual of [(44, 3), 75, 20]-NRT-code) | [i] | ||