Information on Result #1312142
Linear OA(862, 4138, F8, 17) (dual of [4138, 4076, 18]-code), using 33 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 7 times 0, 1, 22 times 0) based on linear OA(858, 4101, F8, 17) (dual of [4101, 4043, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(857, 4096, F8, 17) (dual of [4096, 4039, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(853, 4096, F8, 15) (dual of [4096, 4043, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(81, 5, F8, 1) (dual of [5, 4, 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(862, 4138, F8, 2, 17) (dual of [(4138, 2), 8214, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(862, 4138, F8, 3, 17) (dual of [(4138, 3), 12352, 18]-NRT-code) | [i] | ||
| 3 | Digital (45, 62, 4138)-net over F8 | [i] | ||
| 4 | Linear OOA(862, 2069, F8, 2, 17) (dual of [(2069, 2), 4076, 18]-NRT-code) | [i] | OOA Folding | |