MinT - Information on Result #982115

Information on Result #982115

Linear OOA(8¹⁰⁹, 55, F₈, 3, 59) (dual of [(55, 3), 56, 60]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁰⁹, 110, F₈, 2, 59) (dual of [(110, 2), 111, 60]-NRT-code), using

constructionÂ X applied to AG(2;F,134P) âŠ‚ AG(2;F,147P) [i] based on
1. linear OOA(8⁹⁶, 97, F₈, 2, 59) (dual of [(97, 2), 98, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,134P) [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(8⁸³, 97, F₈, 2, 46) (dual of [(97, 2), 111, 47]-NRT-code), using algebraic-geometric NRT-code AG(2;F,147P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
3. linear OOA(8¹³, 13, F₈, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹³, 14, F₈, 2, 12) (dual of [(14, 2), 15, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,15P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [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.