Information on Result #686204
Linear OA(8145, 2097185, F8, 23) (dual of [2097185, 2097040, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,9]) based on
- linear OA(8141, 2097153, F8, 23) (dual of [2097153, 2097012, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), 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(8146, 2097186, F8, 23) (dual of [2097186, 2097040, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8145, 1932007, F8, 2, 23) (dual of [(1932007, 2), 3863869, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8145, 1932007, F8, 3, 23) (dual of [(1932007, 3), 5795876, 24]-NRT-code) | [i] | ||
| 4 | Digital (122, 145, 1932007)-net over F8 | [i] | ||
| 5 | Linear OA(8146, 2097187, F8, 23) (dual of [2097187, 2097041, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(8145, 1048592, F8, 2, 23) (dual of [(1048592, 2), 2097039, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8145, 699061, F8, 3, 23) (dual of [(699061, 3), 2097038, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(8145, 190653, F8, 23, 23) (dual of [(190653, 23), 4384874, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |