MinT - Information on Result #982106

Information on Result #982106

Linear OOA(8⁸⁵, 38, F₈, 3, 59) (dual of [(38, 3), 29, 60]-NRT-code), using OOA 2-folding based on linear OOA(8⁸⁵, 76, F₈, 2, 59) (dual of [(76, 2), 67, 60]-NRT-code), using

constructionÂ X applied to AG(2;F,68P) âŠ‚ AG(2;F,80P) [i] based on
1. linear OOA(8⁷³, 64, F₈, 2, 59) (dual of [(64, 2), 55, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,68P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
  - the Suzuki function field over F₈ [i]
2. linear OOA(8⁶¹, 64, F₈, 2, 47) (dual of [(64, 2), 67, 48]-NRT-code), using algebraic-geometric NRT-code AG(2;F,80P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹², 12, F₈, 2, 11) (dual of [(12, 2), 12, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹², 14, F₈, 2, 11) (dual of [(14, 2), 16, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,16P) [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.