Information on Result #1324060
Linear OA(4202, 65603, F4, 31) (dual of [65603, 65401, 32]-code), using construction X with Varšamov bound based on
- linear OA(4199, 65598, F4, 31) (dual of [65598, 65399, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(22) [i] based on
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(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(30) ⊂ Ce(22) [i] based on
- linear OA(4199, 65600, F4, 29) (dual of [65600, 65401, 30]-code), using Gilbert–Varšamov bound and bm = 4199 > Vbs−1(k−1) = 55710 285515 175927 772784 347960 437459 083294 992050 760408 056883 157147 541959 651478 209430 597197 554085 291818 111297 624084 223761 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 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(4202, 32801, F4, 2, 31) (dual of [(32801, 2), 65400, 32]-NRT-code) | [i] | OOA Folding | |