Information on Result #1323944
Linear OA(4153, 65601, F4, 23) (dual of [65601, 65448, 24]-code), using construction X with Varšamov bound based on
- linear OA(4151, 65598, F4, 23) (dual of [65598, 65447, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(14) [i] based on
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(414, 62, F4, 7) (dual of [62, 48, 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(4151, 65599, F4, 21) (dual of [65599, 65448, 22]-code), using Gilbert–Varšamov bound and bm = 4151 > Vbs−1(k−1) = 3110 989683 498237 211267 333276 558121 313606 589535 567289 056678 740726 533973 973555 303373 801811 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 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: 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(4153, 65601, F4, 2, 23) (dual of [(65601, 2), 131049, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4153, 65601, F4, 3, 23) (dual of [(65601, 3), 196650, 24]-NRT-code) | [i] | ||
| 3 | Digital (130, 153, 65601)-net over F4 | [i] | ||