Information on Result #700716
Linear OA(322, 89, F3, 8) (dual of [89, 67, 9]-code), using construction XX applied to C1 = C({0,1,2,4,53}), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,53}) based on
- linear OA(317, 80, F3, 6) (dual of [80, 63, 7]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,53}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (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(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(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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(31, 5, F3, 1) (dual of [5, 4, 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
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(322, 66, F3, 2, 8) (dual of [(66, 2), 110, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(322, 66, F3, 3, 8) (dual of [(66, 3), 176, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(322, 66, F3, 4, 8) (dual of [(66, 4), 242, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(322, 66, F3, 5, 8) (dual of [(66, 5), 308, 9]-NRT-code) | [i] | ||
| 5 | Digital (14, 22, 66)-net over F3 | [i] | ||
| 6 | Linear OOA(322, 44, F3, 2, 8) (dual of [(44, 2), 66, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(322, 29, F3, 3, 8) (dual of [(29, 3), 65, 9]-NRT-code) | [i] | ||