Information on Result #1448494
Linear OOA(8167, 32797, F8, 2, 37) (dual of [(32797, 2), 65427, 38]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8167, 32797, F8, 37) (dual of [32797, 32630, 38]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8165, 32793, F8, 37) (dual of [32793, 32628, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(8161, 32769, F8, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(8141, 32769, F8, 33) (dual of [32769, 32628, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(8165, 32795, F8, 36) (dual of [32795, 32630, 37]-code), using Gilbert–Varšamov bound and bm = 8165 > Vbs−1(k−1) = 4066 177743 899096 602683 464230 709518 922722 918364 629672 474993 222635 458244 035026 712435 827672 893229 011831 204599 818743 978020 956346 979582 723990 639619 788800 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 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(8165, 32793, F8, 37) (dual of [32793, 32628, 38]-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(8167, 16398, F8, 3, 37) (dual of [(16398, 3), 49027, 38]-NRT-code) | [i] | OOA Folding | |