Information on Result #700735
Linear OA(336, 99, F3, 12) (dual of [99, 63, 13]-code), using construction XX applied to C1 = C({0,1,2,4,5,53}), C2 = C([0,10]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,53}) based on
- linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,53}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(327, 80, F3, 11) (dual of [80, 53, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(331, 80, F3, 12) (dual of [80, 49, 13]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,53}, and minimum distance d ≥ |{−1,0,…,10}|+1 = 13 (BCH-bound) [i]
- linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(30, 4, F3, 0) (dual of [4, 4, 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
- linear OA(35, 15, F3, 3) (dual of [15, 10, 4]-code or 15-cap in PG(4,3)), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(336, 98, F3, 2, 12) (dual of [(98, 2), 160, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(336, 98, F3, 3, 12) (dual of [(98, 3), 258, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(336, 98, F3, 4, 12) (dual of [(98, 4), 356, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(336, 98, F3, 5, 12) (dual of [(98, 5), 454, 13]-NRT-code) | [i] | ||
| 5 | Digital (24, 36, 98)-net over F3 | [i] | ||
| 6 | Linear OOA(336, 49, F3, 2, 12) (dual of [(49, 2), 62, 13]-NRT-code) | [i] | OOA Folding | |