Information on Result #637603
Linear OA(558, 78, F5, 33) (dual of [78, 20, 34]-code), using concatenation of two codes based on
- linear OA(2516, 26, F25, 16) (dual of [26, 10, 17]-code or 26-arc in PG(15,25)), using
- extended Reed–Solomon code RSe(10,25) [i]
- algebraic-geometric code AG(F, Q+3P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F,3P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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 OA(558, 78, F5, 32) (dual of [78, 20, 33]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(559, 79, F5, 33) (dual of [79, 20, 34]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(560, 80, F5, 33) (dual of [80, 20, 34]-code) | [i] | ||
| 4 | Linear OA(561, 81, F5, 33) (dual of [81, 20, 34]-code) | [i] | ||
| 5 | Linear OA(557, 77, F5, 32) (dual of [77, 20, 33]-code) | [i] | Truncation | |
| 6 | Linear OA(559, 80, F5, 33) (dual of [80, 21, 34]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(558, 39, F5, 2, 33) (dual of [(39, 2), 20, 34]-NRT-code) | [i] | OOA Folding | |