Information on Result #677802
Linear OA(323, 88, F3, 8) (dual of [88, 65, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(6) ⊂ Ce(4) based on
- linear OA(321, 81, F3, 8) (dual of [81, 60, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(317, 81, F3, 7) (dual of [81, 64, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(313, 81, F3, 5) (dual of [81, 68, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 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, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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.
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(323, 80, F3, 2, 8) (dual of [(80, 2), 137, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(323, 80, F3, 3, 8) (dual of [(80, 3), 217, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(323, 80, F3, 4, 8) (dual of [(80, 4), 297, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(323, 80, F3, 5, 8) (dual of [(80, 5), 377, 9]-NRT-code) | [i] | ||
| 5 | Digital (15, 23, 80)-net over F3 | [i] | ||