Information on Result #1431810
Linear OOA(4228, 11559, F4, 2, 43) (dual of [(11559, 2), 22890, 44]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4228, 11559, F4, 43) (dual of [11559, 11331, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(4228, 16402, F4, 43) (dual of [16402, 16174, 44]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4226, 16400, F4, 43) (dual of [16400, 16174, 44]-code), using
- construction X applied to C([0,21]) ⊂ C([0,20]) [i] based on
- linear OA(4225, 16385, F4, 43) (dual of [16385, 16160, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(41, 15, F4, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,21]) ⊂ C([0,20]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4226, 16400, F4, 43) (dual of [16400, 16174, 44]-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(4228, 5779, F4, 3, 43) (dual of [(5779, 3), 17109, 44]-NRT-code) | [i] | OOA Folding | |