Information on Result #1545137
Linear OOA(4243, 65627, F4, 3, 37) (dual of [(65627, 3), 196638, 38]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4243, 65627, F4, 37) (dual of [65627, 65384, 38]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4241, 65624, F4, 37) (dual of [65624, 65383, 38]-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(424, 88, F4, 10) (dual of [88, 64, 11]-code), using
- construction X applied to Ce(36) ⊂ Ce(25) [i] based on
- linear OA(4241, 65625, F4, 35) (dual of [65625, 65384, 36]-code), using Gilbert–Varšamov bound and bm = 4241 > Vbs−1(k−1) = 3376 381935 288313 800674 534347 103599 811112 648911 682478 925694 505556 189333 786571 998350 821227 900770 850197 222332 426988 499930 349557 614571 798864 379802 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4241, 65624, F4, 37) (dual of [65624, 65383, 38]-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(4243, 10937, F4, 39, 37) (dual of [(10937, 39), 426300, 38]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |