MinT - Information on Result #1049224

Information on Result #1049224

Linear OOA(8¹⁵³, 136, F₈, 3, 76) (dual of [(136, 3), 255, 77]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵⁶, 67, F₈, 3, 38) (dual of [(67, 3), 145, 39]-NRT-code), using
- constructionÂ X applied to AG(3;F,153P) âŠ‚ AG(3;F,158P) [i] based on
  1. linear OOA(8⁵², 64, F₈, 3, 38) (dual of [(64, 3), 140, 39]-NRT-code), using algebraic-geometric NRT-code AG(3;F,153P) [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(8⁴⁷, 64, F₈, 3, 33) (dual of [(64, 3), 145, 34]-NRT-code), using algebraic-geometric NRT-code AG(3;F,158P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁴, 3, F₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;20,8) [i]
linear OOA(8⁹⁷, 69, F₈, 3, 76) (dual of [(69, 3), 110, 77]-NRT-code), using
- constructionÂ X applied to AG(3;F,115P) âŠ‚ AG(3;F,123P) [i] based on
  1. linear OOA(8⁹⁰, 64, F₈, 3, 76) (dual of [(64, 3), 102, 77]-NRT-code), using algebraic-geometric NRT-code AG(3;F,115P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁸², 64, F₈, 3, 68) (dual of [(64, 3), 110, 69]-NRT-code), using algebraic-geometric NRT-code AG(3;F,123P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁷, 5, F₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 3, 7) (dual of [(8, 3), 17, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;17,8) [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.