Information on Result #1298649
Linear OA(3142, 165, F3, 69) (dual of [165, 23, 70]-code), using construction X with Varšamov bound based on
- linear OA(3139, 160, F3, 69) (dual of [160, 21, 70]-code), using
- concatenation of two codes [i] based on
- linear OA(2713, 20, F27, 13) (dual of [20, 7, 14]-code or 20-arc in PG(12,27)), using
- discarding factors / shortening the dual code based on linear OA(2713, 27, F27, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,27)), using
- Reed–Solomon code RS(14,27) [i]
- discarding factors / shortening the dual code based on linear OA(2713, 27, F27, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,27)), using
- linear OA(35, 8, F3, 4) (dual of [8, 3, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(35, 11, F3, 4) (dual of [11, 6, 5]-code), using
- Golay code G(3) [i]
- discarding factors / shortening the dual code based on linear OA(35, 11, F3, 4) (dual of [11, 6, 5]-code), using
- linear OA(2713, 20, F27, 13) (dual of [20, 7, 14]-code or 20-arc in PG(12,27)), using
- concatenation of two codes [i] based on
- linear OA(3139, 162, F3, 67) (dual of [162, 23, 68]-code), using Gilbert–Varšamov bound and bm = 3139 > Vbs−1(k−1) = 1 507832 569242 944520 093526 597351 767515 684829 587058 204008 336390 171011 [i]
- linear OA(31, 3, F3, 1) (dual of [3, 2, 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: 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 OA(3143, 167, F3, 69) (dual of [167, 24, 70]-code) | [i] | Construction X with Varšamov Bound | |