Information on Result #1300380
Linear OA(4164, 65581, F4, 26) (dual of [65581, 65417, 27]-code), using construction X with Varšamov bound based on
- linear OA(4160, 65575, F4, 26) (dual of [65575, 65415, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(25) ⊂ Ce(20) [i] based on
- linear OA(4160, 65577, F4, 23) (dual of [65577, 65417, 24]-code), using Gilbert–Varšamov bound and bm = 4160 > Vbs−1(k−1) = 258706 807085 805411 287921 999638 163698 373839 701395 490487 759055 021397 678018 465196 647804 453085 062514 [i]
- linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)), using
- Reed–Solomon code RS(2,4) [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(4164, 32790, F4, 2, 26) (dual of [(32790, 2), 65416, 27]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4164, 21860, F4, 3, 26) (dual of [(21860, 3), 65416, 27]-NRT-code) | [i] | ||