Information on Result #1522107
Linear OOA(3106, 4584, F3, 3, 18) (dual of [(4584, 3), 13646, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3106, 4584, F3, 18) (dual of [4584, 4478, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3106, 6603, F3, 18) (dual of [6603, 6497, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3105, 6602, F3, 18) (dual of [6602, 6497, 19]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(365, 6562, F3, 13) (dual of [6562, 6497, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(38, 40, F3, 4) (dual of [40, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3105, 6602, F3, 18) (dual of [6602, 6497, 19]-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(3106, 2292, F3, 5, 18) (dual of [(2292, 5), 11354, 19]-NRT-code) | [i] | OOA Folding | |