Information on Result #1410616
Linear OOA(3138, 10909, F3, 2, 21) (dual of [(10909, 2), 21680, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3138, 10909, F3, 21) (dual of [10909, 10771, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3138, 19725, F3, 21) (dual of [19725, 19587, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(3127, 19684, F3, 21) (dual of [19684, 19557, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(391, 19684, F3, 15) (dual of [19684, 19593, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(311, 41, F3, 5) (dual of [41, 30, 6]-code), using
- (u, u+v)-construction [i] based on
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- (u, u+v)-construction [i] based on
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
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(3138, 5454, F3, 4, 21) (dual of [(5454, 4), 21678, 22]-NRT-code) | [i] | OOA Folding | |