Information on Result #700867
Linear OA(356, 127, F3, 19) (dual of [127, 71, 20]-code), using construction X applied to C({1,4,7,8,10,13,16,19,22,25,26}) ⊂ C({1,7,8,10,13,16,19,22,25,26}) based on
- linear OA(355, 121, F3, 20) (dual of [121, 66, 21]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,22,25,26}, and minimum distance d ≥ |{10,30,50,…,27}|+1 = 21 (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(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
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(355, 126, F3, 18) (dual of [126, 71, 19]-code) | [i] | Truncation | |
| 2 | Linear OA(358, 140, F3, 19) (dual of [140, 82, 20]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(359, 148, F3, 19) (dual of [148, 89, 20]-code) | [i] | ||
| 4 | Linear OOA(356, 63, F3, 2, 19) (dual of [(63, 2), 70, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(356, 42, F3, 3, 19) (dual of [(42, 3), 70, 20]-NRT-code) | [i] | ||