MinT - Information on Result #983032

Information on Result #983032

Linear OOA(8¹²⁴, 51, F₈, 3, 82) (dual of [(51, 3), 29, 83]-NRT-code), using OOA 2-folding based on linear OOA(8¹²⁴, 102, F₈, 2, 82) (dual of [(102, 2), 80, 83]-NRT-code), using

constructionÂ X applied to AG(2;F,111P) âŠ‚ AG(2;F,117P) [i] based on
1. linear OOA(8¹¹⁹, 97, F₈, 2, 82) (dual of [(97, 2), 75, 83]-NRT-code), using algebraic-geometric NRT-code AG(2;F,111P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
  - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. linear OOA(8¹¹³, 97, F₈, 2, 76) (dual of [(97, 2), 81, 77]-NRT-code), using algebraic-geometric NRT-code AG(2;F,117P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
3. linear OOA(8⁵, 5, F₈, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁵, 8, F₈, 2, 5) (dual of [(8, 2), 11, 6]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;11,8) [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.