Information on Result #676253
Linear OA(361, 2207, F3, 12) (dual of [2207, 2146, 13]-code), using construction XX applied to Ce(12) ⊂ Ce(9) ⊂ Ce(7) based on
- linear OA(357, 2187, F3, 13) (dual of [2187, 2130, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(343, 2187, F3, 10) (dual of [2187, 2144, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(336, 2187, F3, 8) (dual of [2187, 2151, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 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(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [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(361, 1642, F3, 2, 12) (dual of [(1642, 2), 3223, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(361, 1642, F3, 3, 12) (dual of [(1642, 3), 4865, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(361, 1642, F3, 4, 12) (dual of [(1642, 4), 6507, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(361, 1642, F3, 5, 12) (dual of [(1642, 5), 8149, 13]-NRT-code) | [i] | ||
| 5 | Digital (49, 61, 1642)-net over F3 | [i] | ||