Information on Result #700785
Linear OA(327, 90, F3, 10) (dual of [90, 63, 11]-code), using construction XX applied to C1 = C({0,4,7,14,17,25}), C2 = C({0,4,7,14,17,22}), C3 = C1 + C2 = C({0,4,7,14,17}), and C∩ = C1 ∩ C2 = C({0,4,7,14,17,22,25}) 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 = {0,4,7,14,17,25}, and minimum distance d ≥ |{−7,0,7,…,42}|+1 = 9 (BCH-bound) [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 = {0,4,7,14,17,22}, and minimum distance d ≥ |{−21,−14,−7,…,28}|+1 = 9 (BCH-bound) [i]
- linear OA(325, 80, F3, 10) (dual of [80, 55, 11]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,4,7,14,17,22,25}, and minimum distance d ≥ |{−21,−14,−7,…,42}|+1 = 11 (BCH-bound) [i]
- 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 = {0,4,7,14,17}, and minimum distance d ≥ |{−7,0,7,…,28}|+1 = 7 (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(327, 45, F3, 2, 10) (dual of [(45, 2), 63, 11]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(327, 30, F3, 3, 10) (dual of [(30, 3), 63, 11]-NRT-code) | [i] | ||