Information on Result #1544744
Linear OOA(4239, 65623, F4, 3, 36) (dual of [(65623, 3), 196630, 37]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4239, 65623, F4, 36) (dual of [65623, 65384, 37]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4238, 65621, F4, 36) (dual of [65621, 65383, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(25) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 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(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to Ce(36) ⊂ Ce(25) [i] based on
- linear OA(4238, 65622, F4, 35) (dual of [65622, 65384, 36]-code), using Gilbert–Varšamov bound and bm = 4238 > Vbs−1(k−1) = 3371 136658 375896 380319 163828 038076 763719 410675 457144 798498 460197 877380 082151 645319 990068 788473 997048 970829 631463 274430 050502 966393 289994 152868 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4238, 65621, F4, 36) (dual of [65621, 65383, 37]-code), 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(4239, 10937, F4, 39, 36) (dual of [(10937, 39), 426304, 37]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |