Information on Result #675731
Linear OA(3245, 3289, F3, 47) (dual of [3289, 3044, 48]-code), using construction X applied to Ce(46) ⊂ Ce(45) based on
- linear OA(3245, 3281, F3, 47) (dual of [3281, 3036, 48]-code), using an extension Ce(46) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3237, 3281, F3, 46) (dual of [3281, 3044, 47]-code), using an extension Ce(45) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 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
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 OA(3246, 3290, F3, 47) (dual of [3290, 3044, 48]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3245, 3289, F3, 2, 47) (dual of [(3289, 2), 6333, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3245, 3289, F3, 3, 47) (dual of [(3289, 3), 9622, 48]-NRT-code) | [i] | ||
| 4 | Linear OOA(3245, 3289, F3, 4, 47) (dual of [(3289, 4), 12911, 48]-NRT-code) | [i] | ||
| 5 | Linear OOA(3245, 3289, F3, 5, 47) (dual of [(3289, 5), 16200, 48]-NRT-code) | [i] | ||
| 6 | Digital (198, 245, 3289)-net over F3 | [i] | ||
| 7 | Linear OA(3246, 3307, F3, 47) (dual of [3307, 3061, 48]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(3247, 3343, F3, 47) (dual of [3343, 3096, 48]-code) | [i] | ||
| 9 | Linear OA(3248, 3400, F3, 47) (dual of [3400, 3152, 48]-code) | [i] | ||
| 10 | Linear OA(3246, 3291, F3, 47) (dual of [3291, 3045, 48]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(3245, 1644, F3, 2, 47) (dual of [(1644, 2), 3043, 48]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3245, 1096, F3, 3, 47) (dual of [(1096, 3), 3043, 48]-NRT-code) | [i] | ||
| 13 | Linear OOA(3245, 822, F3, 4, 47) (dual of [(822, 4), 3043, 48]-NRT-code) | [i] | ||
| 14 | Linear OOA(3245, 657, F3, 5, 47) (dual of [(657, 5), 3040, 48]-NRT-code) | [i] | ||