Information on Result #630135
Linear OA(2140, 176, F2, 51) (dual of [176, 36, 52]-code), using concatenation of two codes based on
- linear OA(1613, 22, F16, 12) (dual of [22, 9, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(1613, 24, F16, 12) (dual of [24, 11, 13]-code), using
- extended algebraic-geometric code AGe(F,11P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(1613, 24, F16, 12) (dual of [24, 11, 13]-code), using
- linear OA(24, 8, F2, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), 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(2140, 176, F2, 50) (dual of [176, 36, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2140, 176, F2, 49) (dual of [176, 36, 50]-code) | [i] | ||
| 3 | Linear OA(2140, 176, F2, 48) (dual of [176, 36, 49]-code) | [i] | ||
| 4 | Linear OA(2141, 177, F2, 51) (dual of [177, 36, 52]-code) | [i] | Code Embedding in Larger Space | |
| 5 | Linear OA(2139, 175, F2, 50) (dual of [175, 36, 51]-code) | [i] | Truncation | |
| 6 | Linear OA(2138, 174, F2, 49) (dual of [174, 36, 50]-code) | [i] | ||
| 7 | Linear OA(2137, 173, F2, 48) (dual of [173, 36, 49]-code) | [i] | ||
| 8 | Linear OOA(2140, 88, F2, 2, 51) (dual of [(88, 2), 36, 52]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(2140, 58, F2, 3, 51) (dual of [(58, 3), 34, 52]-NRT-code) | [i] | ||