Information on Result #675744
Linear OA(3239, 3292, F3, 46) (dual of [3292, 3053, 47]-code), using construction XX applied to Ce(45) ⊂ Ce(43) ⊂ Ce(42) based on
- 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(3229, 3281, F3, 44) (dual of [3281, 3052, 45]-code), using an extension Ce(43) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3221, 3281, F3, 43) (dual of [3281, 3060, 44]-code), using an extension Ce(42) of the narrow-sense BCH-code C(I) with length 3280 | 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3239, 3245, F3, 2, 46) (dual of [(3245, 2), 6251, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3239, 3245, F3, 3, 46) (dual of [(3245, 3), 9496, 47]-NRT-code) | [i] | ||
| 3 | Linear OOA(3239, 3245, F3, 4, 46) (dual of [(3245, 4), 12741, 47]-NRT-code) | [i] | ||
| 4 | Linear OOA(3239, 3245, F3, 5, 46) (dual of [(3245, 5), 15986, 47]-NRT-code) | [i] | ||
| 5 | Digital (193, 239, 3245)-net over F3 | [i] | ||
| 6 | Linear OA(3240, 3296, F3, 46) (dual of [3296, 3056, 47]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OOA(3239, 1646, F3, 2, 46) (dual of [(1646, 2), 3053, 47]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3239, 1097, F3, 3, 46) (dual of [(1097, 3), 3052, 47]-NRT-code) | [i] | ||
| 9 | Linear OOA(3239, 823, F3, 4, 46) (dual of [(823, 4), 3053, 47]-NRT-code) | [i] | ||