Information on Result #1029740
Linear OOA(2138, 72, F2, 3, 51) (dual of [(72, 3), 78, 52]-NRT-code), using concatenation of two NRT-codes based on
- linear OOA(828, 18, F8, 3, 25) (dual of [(18, 3), 26, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(828, 24, F8, 3, 25) (dual of [(24, 3), 44, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,46P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- extended algebraic-geometric NRT-code AGe(3;F,46P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OOA(828, 24, F8, 3, 25) (dual of [(24, 3), 44, 26]-NRT-code), using
- linear OA(21, 4, F2, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2138, 72, F2, 3, 50) (dual of [(72, 3), 78, 51]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2139, 72, F2, 3, 51) (dual of [(72, 3), 77, 52]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2140, 72, F2, 3, 51) (dual of [(72, 3), 76, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(2137, 71, F2, 3, 50) (dual of [(71, 3), 76, 51]-NRT-code) | [i] | Truncation for OOAs | |
| 5 | Linear OOA(2138, 36, F2, 5, 51) (dual of [(36, 5), 42, 52]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2138, 36, F2, 6, 51) (dual of [(36, 6), 78, 52]-NRT-code) | [i] | ||