Information on Result #675232
Linear OA(3130, 19731, F3, 20) (dual of [19731, 19601, 21]-code), using construction X applied to Ce(19) ⊂ Ce(13) based on
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(382, 19683, F3, 14) (dual of [19683, 19601, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(312, 48, F3, 5) (dual of [48, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(312, 54, F3, 5) (dual of [54, 42, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(312, 54, F3, 5) (dual of [54, 42, 6]-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(3130, 9902, F3, 2, 20) (dual of [(9902, 2), 19674, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3130, 9902, F3, 3, 20) (dual of [(9902, 3), 29576, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(3130, 9902, F3, 4, 20) (dual of [(9902, 4), 39478, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(3130, 9902, F3, 5, 20) (dual of [(9902, 5), 49380, 21]-NRT-code) | [i] | ||
| 5 | Digital (110, 130, 9902)-net over F3 | [i] | ||
| 6 | Linear OOA(3130, 6577, F3, 3, 20) (dual of [(6577, 3), 19601, 21]-NRT-code) | [i] | OOA Folding | |