Information on Result #1650026
Linear OOA(3222, 164586, F3, 5, 27) (dual of [(164586, 5), 822708, 28]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3222, 164586, F3, 3, 27) (dual of [(164586, 3), 493536, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3222, 177157, F3, 3, 27) (dual of [(177157, 3), 531249, 28]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3219, 177156, F3, 3, 27) (dual of [(177156, 3), 531249, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3219, 531468, F3, 27) (dual of [531468, 531249, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3218, 531467, F3, 27) (dual of [531467, 531249, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(3217, 531442, F3, 27) (dual of [531442, 531225, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3193, 531442, F3, 25) (dual of [531442, 531249, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(31, 25, F3, 1) (dual of [25, 24, 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([0,13]) ⊂ C([0,12]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3218, 531467, F3, 27) (dual of [531467, 531249, 28]-code), using
- OOA 3-folding [i] based on linear OA(3219, 531468, F3, 27) (dual of [531468, 531249, 28]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3219, 177156, F3, 3, 27) (dual of [(177156, 3), 531249, 28]-NRT-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(3222, 54861, F3, 35, 27) (dual of [(54861, 35), 1919913, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |