Information on Result #2678570
Linear OOA(3247, 59058, F3, 3, 33) (dual of [(59058, 3), 176927, 34]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3244, 59057, F3, 3, 33) (dual of [(59057, 3), 176927, 34]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3244, 177171, F3, 33) (dual of [177171, 176927, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(3243, 177148, F3, 33) (dual of [177148, 176905, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3221, 177148, F3, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(31, 23, F3, 1) (dual of [23, 22, 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 X applied to C([0,16]) ⊂ C([0,15]) [i] based on
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(3247, 59058, F3, 4, 33) (dual of [(59058, 4), 235985, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3247, 59058, F3, 5, 33) (dual of [(59058, 5), 295043, 34]-NRT-code) | [i] | ||
| 3 | Digital (214, 247, 59058)-net over F3 | [i] | ||