Information on Result #1312392
Linear OA(8112, 4180, F8, 31) (dual of [4180, 4068, 32]-code), using 73 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0, 1, 62 times 0) based on linear OA(8110, 4105, F8, 31) (dual of [4105, 3995, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(8109, 4096, F8, 31) (dual of [4096, 3987, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8101, 4096, F8, 29) (dual of [4096, 3995, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-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(8112, 4180, F8, 2, 31) (dual of [(4180, 2), 8248, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8112, 4180, F8, 3, 31) (dual of [(4180, 3), 12428, 32]-NRT-code) | [i] | ||
| 3 | Digital (81, 112, 4180)-net over F8 | [i] | ||
| 4 | Linear OOA(8112, 2090, F8, 2, 31) (dual of [(2090, 2), 4068, 32]-NRT-code) | [i] | OOA Folding | |