Information on Result #1312338
Linear OA(8104, 4731, F8, 28) (dual of [4731, 4627, 29]-code), using 624 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0, 1, 36 times 0, 1, 90 times 0, 1, 187 times 0, 1, 290 times 0) based on linear OA(897, 4100, F8, 28) (dual of [4100, 4003, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(897, 4096, F8, 28) (dual of [4096, 3999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(893, 4096, F8, 27) (dual of [4096, 4003, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(8104, 4731, F8, 2, 28) (dual of [(4731, 2), 9358, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8104, 4731, F8, 3, 28) (dual of [(4731, 3), 14089, 29]-NRT-code) | [i] | ||
| 3 | Digital (76, 104, 4731)-net over F8 | [i] | ||
| 4 | Linear OOA(8104, 2365, F8, 2, 28) (dual of [(2365, 2), 4626, 29]-NRT-code) | [i] | OOA Folding | |