Information on Result #1557550
Linear OOA(8146, 2097187, F8, 3, 23) (dual of [(2097187, 3), 6291415, 24]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8146, 2097187, F8, 23) (dual of [2097187, 2097041, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8145, 2097185, F8, 23) (dual of [2097185, 2097040, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] 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
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(8145, 2097186, F8, 22) (dual of [2097186, 2097041, 23]-code), using Gilbert–Varšamov bound and bm = 8145 > Vbs−1(k−1) = 62093 145466 702123 406103 014560 578405 360638 098480 021164 766781 354407 003667 699228 959687 395769 078965 316525 242992 250299 145786 904866 792184 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8145, 2097185, F8, 23) (dual of [2097185, 2097040, 24]-code), 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(8146, 524296, F8, 27, 23) (dual of [(524296, 27), 14155846, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |