Information on Result #2270474
Linear OA(451, 4112, F4, 11) (dual of [4112, 4061, 12]-code), using 1 times code embedding in larger space based on linear OA(450, 4111, F4, 11) (dual of [4111, 4061, 12]-code), using
- construction X4 applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(449, 4097, F4, 11) (dual of [4097, 4048, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(437, 4097, F4, 9) (dual of [4097, 4060, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
- dual of repetition code with length 14 [i]
- linear OA(41, 14, F4, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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 OOA(451, 3051, F4, 2, 11) (dual of [(3051, 2), 6051, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(451, 3051, F4, 3, 11) (dual of [(3051, 3), 9102, 12]-NRT-code) | [i] | ||
| 3 | Digital (40, 51, 3051)-net over F4 | [i] | ||
| 4 | Linear OOA(451, 2056, F4, 2, 11) (dual of [(2056, 2), 4061, 12]-NRT-code) | [i] | OOA Folding | |