MinT - Information on Result #2641388

Information on Result #2641388

Linear OOA(5¹³⁹, 53, F₅, 3, 112) (dual of [(53, 3), 20, 113]-NRT-code), using strength reduction based on linear OOA(5¹³⁹, 53, F₅, 3, 113) (dual of [(53, 3), 20, 114]-NRT-code), using

constructionÂ X applied to AG(3;F,36P) âŠ‚ AG(3;F,41P) [i] based on
1. linear OOA(5¹³⁵, 50, F₅, 3, 113) (dual of [(50, 3), 15, 114]-NRT-code), using algebraic-geometric NRT-code AG(3;F,36P) [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(5¹³⁰, 50, F₅, 3, 108) (dual of [(50, 3), 20, 109]-NRT-code), using algebraic-geometric NRT-code AG(3;F,41P) [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51 (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: 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

None.