Information on Result #1034824
Linear OOA(4178, 77, F4, 3, 110) (dual of [(77, 3), 53, 111]-NRT-code), using construction X applied to AG(3;F,84P) ⊂ AG(3;F,101P) based on
- linear OOA(4159, 65, F4, 3, 110) (dual of [(65, 3), 36, 111]-NRT-code), using algebraic-geometric NRT-code AG(3;F,84P) [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- linear OOA(4142, 65, F4, 3, 93) (dual of [(65, 3), 53, 94]-NRT-code), using algebraic-geometric NRT-code AG(3;F,101P) [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66 (see above)
- linear OOA(419, 12, F4, 3, 16) (dual of [(12, 3), 17, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(419, 14, F4, 3, 16) (dual of [(14, 3), 23, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,25P) [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- discarding factors / shortening the dual code based on linear OOA(419, 14, F4, 3, 16) (dual of [(14, 3), 23, 17]-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(4178, 77, F4, 3, 109) (dual of [(77, 3), 53, 110]-NRT-code) | [i] | Strength Reduction for OOAs | |