Information on Result #700772
Linear OA(319, 90, F3, 7) (dual of [90, 71, 8]-code), using construction XX applied to C1 = C({0,7,17,22}), C2 = C({0,7,14,17}), C3 = C1 + C2 = C({0,7,17}), and C∩ = C1 ∩ C2 = C({0,7,14,17,22}) based on
- linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,7,17,22}, and minimum distance d ≥ |{−21,−14,−7,0,7}|+1 = 6 (BCH-bound) [i]
- linear OA(313, 80, F3, 5) (dual of [80, 67, 6]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,7,14,17}, and minimum distance d ≥ |{−7,0,7,14,21}|+1 = 6 (BCH-bound) [i]
- linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,7,14,17,22}, and minimum distance d ≥ |{−21,−14,−7,…,21}|+1 = 8 (BCH-bound) [i]
- linear OA(39, 80, F3, 3) (dual of [80, 71, 4]-code or 80-cap in PG(8,3)), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,7,17}, and minimum distance d ≥ |{−7,0,7}|+1 = 4 (BCH-bound) [i]
- 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
- linear OA(31, 5, F3, 1) (dual of [5, 4, 2]-code) (see above)
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(319, 45, F3, 2, 7) (dual of [(45, 2), 71, 8]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(319, 30, F3, 3, 7) (dual of [(30, 3), 71, 8]-NRT-code) | [i] | ||