Information on Result #687055
Linear OA(882, 4106, F8, 23) (dual of [4106, 4024, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(881, 4097, F8, 23) (dual of [4097, 4016, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- 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(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(883, 4107, F8, 23) (dual of [4107, 4024, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(882, 3761, F8, 2, 23) (dual of [(3761, 2), 7440, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(882, 3761, F8, 3, 23) (dual of [(3761, 3), 11201, 24]-NRT-code) | [i] | ||
| 4 | Digital (59, 82, 3761)-net over F8 | [i] | ||
| 5 | Linear OA(883, 4108, F8, 23) (dual of [4108, 4025, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(882, 2053, F8, 2, 23) (dual of [(2053, 2), 4024, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(882, 1368, F8, 3, 23) (dual of [(1368, 3), 4022, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(882, 373, F8, 23, 23) (dual of [(373, 23), 8497, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |