Information on Result #1530437
Linear OOA(3223, 8512, F3, 3, 37) (dual of [(8512, 3), 25313, 38]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3223, 8512, F3, 2, 37) (dual of [(8512, 2), 16801, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 9854, F3, 2, 37) (dual of [(9854, 2), 19485, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3223, 19708, F3, 37) (dual of [19708, 19485, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(3217, 19684, F3, 37) (dual of [19684, 19467, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3199, 19684, F3, 33) (dual of [19684, 19485, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(36, 24, F3, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- OOA 2-folding [i] based on linear OA(3223, 19708, F3, 37) (dual of [19708, 19485, 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(3223, 4256, F3, 5, 37) (dual of [(4256, 5), 21057, 38]-NRT-code) | [i] | OOA Folding | |