Information on Result #1408542
Linear OOA(392, 1744, F3, 2, 18) (dual of [(1744, 2), 3396, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(392, 1744, F3, 18) (dual of [1744, 1652, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(392, 2216, F3, 18) (dual of [2216, 2124, 19]-code), using
- construction XX applied to Ce(18) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- linear OA(385, 2187, F3, 19) (dual of [2187, 2102, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(364, 2187, F3, 14) (dual of [2187, 2123, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(357, 2187, F3, 13) (dual of [2187, 2130, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(18) ⊂ Ce(13) ⊂ Ce(12) [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(392, 872, F3, 3, 18) (dual of [(872, 3), 2524, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(392, 872, F3, 4, 18) (dual of [(872, 4), 3396, 19]-NRT-code) | [i] | ||