MinT - Information on Result #983147

Information on Result #983147

Linear OOA(8¹²⁹, 52, F₈, 3, 85) (dual of [(52, 3), 27, 86]-NRT-code), using OOA 2-folding based on linear OOA(8¹²⁹, 104, F₈, 2, 85) (dual of [(104, 2), 79, 86]-NRT-code), using

constructionÂ X applied to AG(2;F,108P) âŠ‚ AG(2;F,116P) [i] based on
1. linear OOA(8¹²², 97, F₈, 2, 85) (dual of [(97, 2), 72, 86]-NRT-code), using algebraic-geometric NRT-code AG(2;F,108P) [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(8¹¹⁴, 97, F₈, 2, 77) (dual of [(97, 2), 80, 78]-NRT-code), using algebraic-geometric NRT-code AG(2;F,116P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
3. linear OOA(8⁷, 7, F₈, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 2, 7) (dual of [(8, 2), 9, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;9,8) [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.