Information on Result #1300972
Linear OA(4233, 1048629, F4, 30) (dual of [1048629, 1048396, 31]-code), using construction X with Varšamov bound based on
- linear OA(4229, 1048624, F4, 30) (dual of [1048624, 1048395, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(4229, 1048625, F4, 26) (dual of [1048625, 1048396, 27]-code), using Gilbert–Varšamov bound and bm = 4229 > Vbs−1(k−1) = 178961 546401 852405 455426 586756 267837 861977 092114 275078 766868 341572 553096 033004 879898 930985 635370 240175 131686 070758 877667 963169 230325 012078 [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(4233, 349543, F4, 3, 30) (dual of [(349543, 3), 1048396, 31]-NRT-code) | [i] | OOA Folding | |