Information on Result #1301022
Linear OA(4236, 65580, F4, 38) (dual of [65580, 65344, 39]-code), using construction X with Varšamov bound based on
- linear OA(4232, 65575, F4, 38) (dual of [65575, 65343, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- linear OA(4232, 65576, F4, 34) (dual of [65576, 65344, 35]-code), using Gilbert–Varšamov bound and bm = 4232 > Vbs−1(k−1) = 569187 083137 751572 451017 847584 553329 287005 440466 151469 887497 274336 105086 563016 556496 993188 391156 850648 020768 963015 942651 971967 711352 786950 [i]
- linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-cap in PG(2,4)), using
- dual of repetition code with length 4 [i]
- Reed–Solomon code RS(1,4) [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(4236, 32790, F4, 2, 38) (dual of [(32790, 2), 65344, 39]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4236, 21860, F4, 3, 38) (dual of [(21860, 3), 65344, 39]-NRT-code) | [i] | ||