Information on Result #675650
Linear OA(3202, 6595, F3, 37) (dual of [6595, 6393, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(31) ⊂ Ce(30) based on
- linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(38, 33, F3, 4) (dual of [33, 25, 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
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
Mode: Constructive and 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(3202, 3789, F3, 2, 37) (dual of [(3789, 2), 7376, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3202, 3789, F3, 3, 37) (dual of [(3789, 3), 11165, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3202, 3789, F3, 4, 37) (dual of [(3789, 4), 14954, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3202, 3789, F3, 5, 37) (dual of [(3789, 5), 18743, 38]-NRT-code) | [i] | ||
| 5 | Digital (165, 202, 3789)-net over F3 | [i] | ||
| 6 | Linear OOA(3202, 3297, F3, 2, 37) (dual of [(3297, 2), 6392, 38]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3202, 2198, F3, 3, 37) (dual of [(2198, 3), 6392, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(3202, 1319, F3, 5, 37) (dual of [(1319, 5), 6393, 38]-NRT-code) | [i] | ||