Information on Result #630166
Linear OA(2176, 216, F2, 63) (dual of [216, 40, 64]-code), using concatenation of two codes based on
- linear OA(1617, 27, F16, 15) (dual of [27, 10, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(1617, 33, F16, 15) (dual of [33, 16, 16]-code), using
- extended algebraic-geometric code AGe(F,17P) [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- discarding factors / shortening the dual code based on linear OA(1617, 33, F16, 15) (dual of [33, 16, 16]-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(2176, 216, F2, 62) (dual of [216, 40, 63]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2176, 216, F2, 61) (dual of [216, 40, 62]-code) | [i] | ||
| 3 | Linear OA(2176, 216, F2, 60) (dual of [216, 40, 61]-code) | [i] | ||
| 4 | Linear OA(2177, 217, F2, 63) (dual of [217, 40, 64]-code) | [i] | Code Embedding in Larger Space | |
| 5 | Linear OA(2178, 218, F2, 63) (dual of [218, 40, 64]-code) | [i] | ||
| 6 | Linear OA(2179, 219, F2, 63) (dual of [219, 40, 64]-code) | [i] | ||
| 7 | Linear OA(2175, 215, F2, 62) (dual of [215, 40, 63]-code) | [i] | Truncation | |
| 8 | Linear OA(2174, 214, F2, 61) (dual of [214, 40, 62]-code) | [i] | ||
| 9 | Linear OA(2173, 213, F2, 60) (dual of [213, 40, 61]-code) | [i] | ||
| 10 | Linear OOA(2176, 108, F2, 2, 63) (dual of [(108, 2), 40, 64]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(2176, 72, F2, 3, 63) (dual of [(72, 3), 40, 64]-NRT-code) | [i] | ||