Information on Result #677489
Linear OA(343, 251, F3, 13) (dual of [251, 208, 14]-code), using construction XX applied to Ce(12) ⊂ Ce(10) ⊂ Ce(9) based on
- linear OA(341, 243, F3, 13) (dual of [243, 202, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(336, 243, F3, 11) (dual of [243, 207, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(331, 243, F3, 10) (dual of [243, 212, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 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(343, 154, F3, 2, 13) (dual of [(154, 2), 265, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(343, 154, F3, 3, 13) (dual of [(154, 3), 419, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(343, 154, F3, 4, 13) (dual of [(154, 4), 573, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(343, 154, F3, 5, 13) (dual of [(154, 5), 727, 14]-NRT-code) | [i] | ||
| 5 | Digital (30, 43, 154)-net over F3 | [i] | ||