Information on Result #1298350
Linear OA(3112, 129, F3, 57) (dual of [129, 17, 58]-code), using construction X with Varšamov bound based on
- linear OA(3101, 116, F3, 57) (dual of [116, 15, 58]-code), using
- 5 times truncation [i] based on linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,60], and minimum distance d ≥ |{−1,0,…,60}|+1 = 63 (BCH-bound) [i]
- 5 times truncation [i] based on linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using
- linear OA(3101, 118, F3, 49) (dual of [118, 17, 50]-code), using Gilbert–Varšamov bound and bm = 3101 > Vbs−1(k−1) = 793454 720340 065584 430459 558256 354095 595739 458867 [i]
- linear OA(39, 11, F3, 7) (dual of [11, 2, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 12, F3, 7) (dual of [12, 3, 8]-code), using
- 1 times truncation [i] based on linear OA(310, 13, F3, 8) (dual of [13, 3, 9]-code), using
- Simplex code S(3,3) [i]
- the expurgated narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [0,6], and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(310, 13, F3, 8) (dual of [13, 3, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 12, F3, 7) (dual of [12, 3, 8]-code), using
Mode: 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.