Information on Result #1610509
Linear OOA(3222, 19690, F3, 4, 33) (dual of [(19690, 4), 78538, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3222, 19690, F3, 3, 33) (dual of [(19690, 3), 58848, 34]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3222, 59070, F3, 33) (dual of [59070, 58848, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, 59071, F3, 33) (dual of [59071, 58849, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(3221, 59050, F3, 33) (dual of [59050, 58829, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(31, 21, F3, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3222, 59071, F3, 33) (dual of [59071, 58849, 34]-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, 19690, F3, 4, 33) (dual of [(19690, 4), 78537, 34]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3222, 4922, F3, 36, 33) (dual of [(4922, 36), 176970, 34]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |