Information on Result #938090
Linear OOA(16128, 67, F16, 2, 121) (dual of [(67, 2), 6, 122]-NRT-code), using construction X applied to AG(2;F,5P) ⊂ AG(2;F,10P) based on
- linear OOA(16125, 64, F16, 2, 122) (dual of [(64, 2), 3, 123]-NRT-code), using algebraic-geometric NRT-code AG(2;F,5P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F16 [i]
- linear OOA(16122, 64, F16, 2, 117) (dual of [(64, 2), 6, 118]-NRT-code), using algebraic-geometric NRT-code AG(2;F,10P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OOA(163, 3, F16, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(163, 16, F16, 2, 3) (dual of [(16, 2), 29, 4]-NRT-code), using
- Reed–Solomon NRT-code RS(2;29,16) [i]
- discarding factors / shortening the dual code based on linear OOA(163, 16, F16, 2, 3) (dual of [(16, 2), 29, 4]-NRT-code), 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(16128, 67, F16, 2, 120) (dual of [(67, 2), 6, 121]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(16130, 68, F16, 2, 121) (dual of [(68, 2), 6, 122]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(16126, 66, F16, 2, 119) (dual of [(66, 2), 6, 120]-NRT-code) | [i] | Truncation for OOAs | |