Information on Result #631625
Linear OA(385, 112, F3, 39) (dual of [112, 27, 40]-code), using concatenation of two codes based on
- linear OA(2719, 28, F27, 19) (dual of [28, 9, 20]-code or 28-arc in PG(18,27)), using
- extended Reed–Solomon code RSe(9,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(385, 112, F3, 38) (dual of [112, 27, 39]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(386, 113, F3, 39) (dual of [113, 27, 40]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(387, 114, F3, 39) (dual of [114, 27, 40]-code) | [i] | ||
| 4 | Linear OA(388, 115, F3, 39) (dual of [115, 27, 40]-code) | [i] | ||
| 5 | Linear OA(384, 111, F3, 38) (dual of [111, 27, 39]-code) | [i] | Truncation | |
| 6 | Linear OA(388, 117, F3, 39) (dual of [117, 29, 40]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(387, 115, F3, 39) (dual of [115, 28, 40]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(385, 56, F3, 2, 39) (dual of [(56, 2), 27, 40]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(385, 37, F3, 3, 39) (dual of [(37, 3), 26, 40]-NRT-code) | [i] | ||