Information on Result #1312523
Linear OA(8138, 4171, F8, 39) (dual of [4171, 4033, 40]-code), using 70 step Varšamov–Edel lengthening with (ri) = (1, 69 times 0) based on linear OA(8137, 4100, F8, 39) (dual of [4100, 3963, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- linear OA(8137, 4096, F8, 39) (dual of [4096, 3959, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(8133, 4096, F8, 38) (dual of [4096, 3963, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(8138, 4171, F8, 2, 39) (dual of [(4171, 2), 8204, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8138, 4171, F8, 3, 39) (dual of [(4171, 3), 12375, 40]-NRT-code) | [i] | ||
| 3 | Digital (99, 138, 4171)-net over F8 | [i] | ||
| 4 | Linear OOA(8138, 2085, F8, 2, 39) (dual of [(2085, 2), 4032, 40]-NRT-code) | [i] | OOA Folding | |