Information on Result #1298344
Linear OA(3115, 139, F3, 55) (dual of [139, 24, 56]-code), using construction X with Varšamov bound based on
- linear OA(3100, 120, F3, 55) (dual of [120, 20, 56]-code), using
- 1 times truncation [i] based on linear OA(3101, 121, F3, 56) (dual of [121, 20, 57]-code), using
- linear OA(3100, 124, F3, 46) (dual of [124, 24, 47]-code), using Gilbert–Varšamov bound and bm = 3100 > Vbs−1(k−1) = 438821 707461 969487 287948 666745 044695 398100 317755 [i]
- linear OA(311, 15, F3, 8) (dual of [15, 4, 9]-code), using
- construction X applied to C([0,6]) ⊂ C([1,6]) [i] based on
- linear OA(310, 13, F3, 8) (dual of [13, 3, 9]-code), using 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]
- linear OA(39, 13, F3, 6) (dual of [13, 4, 7]-code), using the narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 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
- construction X applied to C([0,6]) ⊂ C([1,6]) [i] based on
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3118, 144, F3, 55) (dual of [144, 26, 56]-code) | [i] | Construction X with Varšamov Bound | |