Information on Result #1429544
Linear OOA(4209, 59948, F4, 2, 32) (dual of [(59948, 2), 119687, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4209, 59948, F4, 32) (dual of [59948, 59739, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(4209, 65601, F4, 32) (dual of [65601, 65392, 33]-code), using
- strength reduction [i] based on linear OA(4209, 65601, F4, 33) (dual of [65601, 65392, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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([0,16]) ⊂ C([0,12]) [i] based on
- strength reduction [i] based on linear OA(4209, 65601, F4, 33) (dual of [65601, 65392, 34]-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(4209, 29974, F4, 3, 32) (dual of [(29974, 3), 89713, 33]-NRT-code) | [i] | OOA Folding | |