Information on Result #1323920
Linear OA(4136, 16444, F4, 23) (dual of [16444, 16308, 24]-code), using construction X with Varšamov bound based on
- linear OA(4134, 16440, F4, 23) (dual of [16440, 16306, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(14) [i] based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(22) ⊂ Ce(14) [i] based on
- linear OA(4134, 16442, F4, 22) (dual of [16442, 16308, 23]-code), using Gilbert–Varšamov bound and bm = 4134 > Vbs−1(k−1) = 6 923582 874662 785998 435914 915822 848927 272983 571982 036525 921694 273644 644840 923356 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(4136, 16444, F4, 2, 23) (dual of [(16444, 2), 32752, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4136, 16444, F4, 3, 23) (dual of [(16444, 3), 49196, 24]-NRT-code) | [i] | ||
| 3 | Digital (113, 136, 16444)-net over F4 | [i] | ||
| 4 | Linear OOA(4136, 8222, F4, 2, 23) (dual of [(8222, 2), 16308, 24]-NRT-code) | [i] | OOA Folding | |