Information on Result #1543618
Linear OOA(4227, 58242, F4, 3, 35) (dual of [(58242, 3), 174499, 36]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4227, 58242, F4, 35) (dual of [58242, 58015, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4227, 65603, F4, 35) (dual of [65603, 65376, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4225, 65601, F4, 35) (dual of [65601, 65376, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4161, 65537, F4, 27) (dual of [65537, 65376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
- an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4225, 65601, F4, 35) (dual of [65601, 65376, 36]-code), using
Mode: 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(4227, 9706, F4, 39, 35) (dual of [(9706, 39), 378307, 36]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |