Information on Result #678902
Linear OA(4184, 16400, F4, 35) (dual of [16400, 16216, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,16]) based on
- linear OA(4183, 16385, F4, 35) (dual of [16385, 16202, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(41, 15, F4, 1) (dual of [15, 14, 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 OA(4185, 16401, F4, 35) (dual of [16401, 16216, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4186, 16402, F4, 35) (dual of [16402, 16216, 36]-code) | [i] | ||
| 3 | Linear OOA(4184, 9544, F4, 2, 35) (dual of [(9544, 2), 18904, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4184, 9544, F4, 3, 35) (dual of [(9544, 3), 28448, 36]-NRT-code) | [i] | ||
| 5 | Digital (149, 184, 9544)-net over F4 | [i] | ||
| 6 | Linear OOA(4184, 8200, F4, 2, 35) (dual of [(8200, 2), 16216, 36]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4184, 5466, F4, 3, 35) (dual of [(5466, 3), 16214, 36]-NRT-code) | [i] | ||