Information on Result #2281167
Linear OA(893, 32781, F8, 21) (dual of [32781, 32688, 22]-code), using 1 times code embedding in larger space based on linear OA(892, 32780, F8, 21) (dual of [32780, 32688, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(891, 32769, F8, 21) (dual of [32769, 32678, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(881, 32769, F8, 19) (dual of [32769, 32688, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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: Constructive and 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(893, 26717, F8, 2, 21) (dual of [(26717, 2), 53341, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(893, 26717, F8, 3, 21) (dual of [(26717, 3), 80058, 22]-NRT-code) | [i] | ||
| 3 | Digital (72, 93, 26717)-net over F8 | [i] | ||
| 4 | Linear OOA(893, 10927, F8, 3, 21) (dual of [(10927, 3), 32688, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(893, 3278, F8, 21, 21) (dual of [(3278, 21), 68745, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |