Information on Result #1312136
Linear OA(851, 744, F8, 17) (dual of [744, 693, 18]-code), using 221 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 18 times 0, 1, 40 times 0, 1, 65 times 0, 1, 84 times 0) based on linear OA(844, 516, F8, 17) (dual of [516, 472, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- 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(840, 512, F8, 15) (dual of [512, 472, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(81, 4, F8, 1) (dual of [4, 3, 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(851, 744, F8, 2, 17) (dual of [(744, 2), 1437, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(851, 744, F8, 3, 17) (dual of [(744, 3), 2181, 18]-NRT-code) | [i] | ||
| 3 | Digital (34, 51, 744)-net over F8 | [i] | ||
| 4 | Linear OOA(851, 372, F8, 2, 17) (dual of [(372, 2), 693, 18]-NRT-code) | [i] | OOA Folding | |