MinT - Information on Result #2718425

Information on Result #2718425

Linear OOA(5¹⁰⁹, 57, F₅, 3, 81) (dual of [(57, 3), 62, 82]-NRT-code), using strength reduction based on linear OOA(5¹⁰⁹, 57, F₅, 3, 82) (dual of [(57, 3), 62, 83]-NRT-code), using

constructionÂ X applied to AG(3;F,79P) âŠ‚ AG(3;F,84P) [i] based on
1. linear OOA(5¹⁰⁵, 54, F₅, 3, 82) (dual of [(54, 3), 57, 83]-NRT-code), using algebraic-geometric NRT-code AG(3;F,79P) [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]
2. linear OOA(5¹⁰⁰, 54, F₅, 3, 77) (dual of [(54, 3), 62, 78]-NRT-code), using algebraic-geometric NRT-code AG(3;F,84P) [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55 (see above)
3. linear OOA(5⁴, 3, F₅, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5⁴, 5, F₅, 3, 4) (dual of [(5, 3), 11, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;11,5) [i]

Mode: 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

None.