MinT - Information on Result #1049377

Information on Result #1049377

Linear OOA(8¹⁷², 136, F₈, 3, 89) (dual of [(136, 3), 236, 90]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶², 67, F₈, 3, 44) (dual of [(67, 3), 139, 45]-NRT-code), using
- constructionÂ X applied to AG(3;F,147P) âŠ‚ AG(3;F,152P) [i] based on
  1. linear OOA(8⁵⁸, 64, F₈, 3, 44) (dual of [(64, 3), 134, 45]-NRT-code), using algebraic-geometric NRT-code AG(3;F,147P) [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(8⁵³, 64, F₈, 3, 39) (dual of [(64, 3), 139, 40]-NRT-code), using algebraic-geometric NRT-code AG(3;F,152P) [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(8¹¹⁰, 69, F₈, 3, 89) (dual of [(69, 3), 97, 90]-NRT-code), using
- constructionÂ X applied to AG(3;F,102P) âŠ‚ AG(3;F,110P) [i] based on
  1. linear OOA(8¹⁰³, 64, F₈, 3, 89) (dual of [(64, 3), 89, 90]-NRT-code), using algebraic-geometric NRT-code AG(3;F,102P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁹⁵, 64, F₈, 3, 81) (dual of [(64, 3), 97, 82]-NRT-code), using algebraic-geometric NRT-code AG(3;F,110P) [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.