Information on Result #1424922
Linear OOA(4164, 5211, F4, 2, 33) (dual of [(5211, 2), 10258, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4164, 5211, F4, 33) (dual of [5211, 5047, 34]-code), using
- 1090 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 24 times 0, 1, 38 times 0, 1, 57 times 0, 1, 83 times 0, 1, 113 times 0, 1, 145 times 0, 1, 174 times 0, 1, 196 times 0, 1, 212 times 0) [i] based on linear OA(4146, 4103, F4, 33) (dual of [4103, 3957, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4139, 4096, F4, 31) (dual of [4096, 3957, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
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, 2605, F4, 3, 33) (dual of [(2605, 3), 7651, 34]-NRT-code) | [i] | OOA Folding | |