Information on Result #1312561
Linear OA(8146, 4105, F8, 42) (dual of [4105, 3959, 43]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(8145, 4100, F8, 42) (dual of [4100, 3955, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(40) [i] based on
- linear OA(8145, 4096, F8, 42) (dual of [4096, 3951, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(8141, 4096, F8, 41) (dual of [4096, 3955, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(80, 4, F8, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(8146, 4105, F8, 2, 42) (dual of [(4105, 2), 8064, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8146, 4105, F8, 3, 42) (dual of [(4105, 3), 12169, 43]-NRT-code) | [i] | ||
| 3 | Digital (104, 146, 4105)-net over F8 | [i] | ||
| 4 | Linear OOA(8146, 2052, F8, 2, 42) (dual of [(2052, 2), 3958, 43]-NRT-code) | [i] | OOA Folding | |