Information on Result #813344
Linear OOA(391, 3286, F3, 2, 17) (dual of [(3286, 2), 6481, 18]-NRT-code), using OOA 2-folding based on linear OA(391, 6572, F3, 17) (dual of [6572, 6481, 18]-code), using
- construction XX applied to Ce(16) ⊂ Ce(15) ⊂ Ce(13) [i] based on
- linear OA(389, 6561, F3, 17) (dual of [6561, 6472, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(381, 6561, F3, 16) (dual of [6561, 6480, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(391, 3250, F3, 3, 17) (dual of [(3250, 3), 9659, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(391, 3250, F3, 4, 17) (dual of [(3250, 4), 12909, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(391, 3250, F3, 5, 17) (dual of [(3250, 5), 16159, 18]-NRT-code) | [i] | ||
| 4 | Digital (74, 91, 3250)-net over F3 | [i] | ||