Information on Result #653573
Linear OA(6477, 183, F64, 67) (dual of [183, 106, 68]-code), using construction X applied to AG(F,108P) ⊂ AG(F,112P) based on
- linear OA(6474, 176, F64, 67) (dual of [176, 102, 68]-code), using algebraic-geometric code AG(F,108P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- linear OA(6470, 176, F64, 63) (dual of [176, 106, 64]-code), using algebraic-geometric code AG(F,112P) [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177 (see above)
- linear OA(643, 7, F64, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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 OA(4231, 549, F4, 67) (dual of [549, 318, 68]-code) | [i] | Trace Code | |
| 2 | Linear OA(8154, 366, F8, 67) (dual of [366, 212, 68]-code) | [i] | ||
| 3 | OA(3293, 183, S32, 67) | [i] | Discarding Parts of the Base for OAs | |
| 4 | Linear OOA(6477, 91, F64, 2, 67) (dual of [(91, 2), 105, 68]-NRT-code) | [i] | OOA Folding | |