Information on Result #1312153
Linear OA(853, 681, F8, 18) (dual of [681, 628, 19]-code), using 159 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 0, 1, 10 times 0, 1, 25 times 0, 1, 47 times 0, 1, 68 times 0) based on linear OA(846, 515, F8, 18) (dual of [515, 469, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(846, 512, F8, 18) (dual of [512, 466, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(843, 512, F8, 17) (dual of [512, 469, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 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(853, 681, F8, 2, 18) (dual of [(681, 2), 1309, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(853, 681, F8, 3, 18) (dual of [(681, 3), 1990, 19]-NRT-code) | [i] | ||
| 3 | Digital (35, 53, 681)-net over F8 | [i] | ||