Information on Result #2273079
Linear OA(4159, 4111, F4, 35) (dual of [4111, 3952, 36]-code), using 1 times code embedding in larger space based on linear OA(4158, 4110, F4, 35) (dual of [4110, 3952, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,16]) [i] based on
- linear OA(4157, 4097, F4, 35) (dual of [4097, 3940, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4145, 4097, F4, 33) (dual of [4097, 3952, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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(4159, 3322, F4, 2, 35) (dual of [(3322, 2), 6485, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4159, 3322, F4, 3, 35) (dual of [(3322, 3), 9807, 36]-NRT-code) | [i] | ||
| 3 | Digital (124, 159, 3322)-net over F4 | [i] | ||