Information on Result #687056
Linear OA(874, 4106, F8, 21) (dual of [4106, 4032, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(873, 4097, F8, 21) (dual of [4097, 4024, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(865, 4097, F8, 19) (dual of [4097, 4032, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [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: 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 OA(875, 4107, F8, 21) (dual of [4107, 4032, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(874, 3330, F8, 2, 21) (dual of [(3330, 2), 6586, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(874, 3330, F8, 3, 21) (dual of [(3330, 3), 9916, 22]-NRT-code) | [i] | ||
| 4 | Digital (53, 74, 3330)-net over F8 | [i] | ||
| 5 | Linear OOA(874, 2053, F8, 2, 21) (dual of [(2053, 2), 4032, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(874, 1368, F8, 3, 21) (dual of [(1368, 3), 4030, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(874, 410, F8, 21, 21) (dual of [(410, 21), 8536, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |