MinT - Information on Result #941154

Information on Result #941154

Linear OOA(8¹⁴⁰, 134, F₈, 2, 71) (dual of [(134, 2), 128, 72]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵², 67, F₈, 2, 35) (dual of [(67, 2), 82, 36]-NRT-code), using
- constructionÂ X applied to AG(2;F,92P) âŠ‚ AG(2;F,96P) [i] based on
  1. linear OOA(8⁴⁹, 64, F₈, 2, 35) (dual of [(64, 2), 79, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,92P) [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(8⁴⁵, 64, F₈, 2, 31) (dual of [(64, 2), 83, 32]-NRT-code), using algebraic-geometric NRT-code AG(2;F,96P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8³, 3, F₈, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8³, 8, F₈, 2, 3) (dual of [(8, 2), 13, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;13,8) [i]
linear OOA(8⁸⁸, 67, F₈, 2, 71) (dual of [(67, 2), 46, 72]-NRT-code), using
- constructionÂ X applied to AG(2;F,56P) âŠ‚ AG(2;F,60P) [i] based on
  1. linear OOA(8⁸⁵, 64, F₈, 2, 71) (dual of [(64, 2), 43, 72]-NRT-code), using algebraic-geometric NRT-code AG(2;F,56P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁸¹, 64, F₈, 2, 67) (dual of [(64, 2), 47, 68]-NRT-code), using algebraic-geometric NRT-code AG(2;F,60P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8³, 3, F₈, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code) (see above)

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.