Information on Result #631527
Linear OA(367, 112, F3, 27) (dual of [112, 45, 28]-code), using concatenation of two codes based on
- linear OA(2713, 28, F27, 13) (dual of [28, 15, 14]-code or 28-arc in PG(12,27)), using
- extended Reed–Solomon code RSe(15,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(31, 4, F3, 1) (dual of [4, 3, 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(367, 112, F3, 26) (dual of [112, 45, 27]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(368, 113, F3, 27) (dual of [113, 45, 28]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(369, 114, F3, 27) (dual of [114, 45, 28]-code) | [i] | ||
| 4 | Linear OA(370, 115, F3, 27) (dual of [115, 45, 28]-code) | [i] | ||
| 5 | Linear OA(371, 116, F3, 27) (dual of [116, 45, 28]-code) | [i] | ||
| 6 | Linear OA(366, 111, F3, 26) (dual of [111, 45, 27]-code) | [i] | Truncation | |
| 7 | Linear OA(370, 118, F3, 27) (dual of [118, 48, 28]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(371, 121, F3, 27) (dual of [121, 50, 28]-code) | [i] | ||
| 9 | Linear OA(372, 125, F3, 27) (dual of [125, 53, 28]-code) | [i] | ||
| 10 | Linear OA(373, 129, F3, 27) (dual of [129, 56, 28]-code) | [i] | ||
| 11 | Linear OA(374, 134, F3, 27) (dual of [134, 60, 28]-code) | [i] | ||
| 12 | Linear OA(375, 139, F3, 27) (dual of [139, 64, 28]-code) | [i] | ||
| 13 | Linear OA(369, 115, F3, 27) (dual of [115, 46, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 14 | Linear OA(370, 117, F3, 27) (dual of [117, 47, 28]-code) | [i] | ||
| 15 | Linear OOA(367, 56, F3, 2, 27) (dual of [(56, 2), 45, 28]-NRT-code) | [i] | OOA Folding | |
| 16 | Linear OOA(367, 37, F3, 3, 27) (dual of [(37, 3), 44, 28]-NRT-code) | [i] | ||