Information on Result #682883
Linear OA(552, 3137, F5, 13) (dual of [3137, 3085, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(551, 3126, F5, 13) (dual of [3126, 3075, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(541, 3126, F5, 11) (dual of [3126, 3085, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(553, 3138, F5, 13) (dual of [3138, 3085, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(554, 3139, F5, 13) (dual of [3139, 3085, 14]-code) | [i] | ||
| 3 | Linear OOA(552, 2129, F5, 2, 13) (dual of [(2129, 2), 4206, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(552, 2129, F5, 3, 13) (dual of [(2129, 3), 6335, 14]-NRT-code) | [i] | ||
| 5 | Digital (39, 52, 2129)-net over F5 | [i] | ||
| 6 | Linear OA(554, 3140, F5, 13) (dual of [3140, 3086, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(552, 1568, F5, 2, 13) (dual of [(1568, 2), 3084, 14]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(552, 1045, F5, 3, 13) (dual of [(1045, 3), 3083, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(552, 522, F5, 13, 13) (dual of [(522, 13), 6734, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |