Information on Result #1324236
Linear OA(4250, 65602, F4, 39) (dual of [65602, 65352, 40]-code), using construction X with Varšamov bound based on
- linear OA(4247, 65598, F4, 39) (dual of [65598, 65351, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(30) [i] based on
- linear OA(4233, 65536, F4, 39) (dual of [65536, 65303, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- 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(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(38) ⊂ Ce(30) [i] based on
- linear OA(4247, 65599, F4, 36) (dual of [65599, 65352, 37]-code), using Gilbert–Varšamov bound and bm = 4247 > Vbs−1(k−1) = 18 720592 305725 780751 465335 080753 962757 674422 989763 513390 768616 048830 544737 873947 284090 354477 045767 727033 450697 173471 370907 769545 310476 632528 765198 [i]
- linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [i]
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(4250, 32801, F4, 2, 39) (dual of [(32801, 2), 65352, 40]-NRT-code) | [i] | OOA Folding | |