Information on Result #2486331
Linear OOA(3113, 9853, F3, 2, 18) (dual of [(9853, 2), 19593, 19]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3111, 9852, F3, 2, 18) (dual of [(9852, 2), 19593, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3111, 19704, F3, 18) (dual of [19704, 19593, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3110, 19703, F3, 18) (dual of [19703, 19593, 19]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3109, 19683, F3, 19) (dual of [19683, 19574, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- dual of repetition code with length 20 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(18) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3110, 19703, F3, 18) (dual of [19703, 19593, 19]-code), using
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(3113, 9853, F3, 3, 18) (dual of [(9853, 3), 29446, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3113, 9853, F3, 4, 18) (dual of [(9853, 4), 39299, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3113, 9853, F3, 5, 18) (dual of [(9853, 5), 49152, 19]-NRT-code) | [i] | ||
| 4 | Digital (95, 113, 9853)-net over F3 | [i] | ||