MinT - Information on Result #941315

Information on Result #941315

Linear OOA(8¹⁶², 141, F₈, 2, 81) (dual of [(141, 2), 120, 82]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶⁰, 70, F₈, 2, 40) (dual of [(70, 2), 80, 41]-NRT-code), using
- constructionÂ X applied to AG(2;F,87P) âŠ‚ AG(2;F,94P) [i] based on
  1. linear OOA(8⁵⁴, 64, F₈, 2, 40) (dual of [(64, 2), 74, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,87P) [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, 2, 33) (dual of [(64, 2), 81, 34]-NRT-code), using algebraic-geometric NRT-code AG(2;F,94P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁶, 6, F₈, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁶, 8, F₈, 2, 6) (dual of [(8, 2), 10, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;10,8) [i]
linear OOA(8¹⁰², 71, F₈, 2, 81) (dual of [(71, 2), 40, 82]-NRT-code), using
- constructionÂ X applied to AG(2;F,46P) âŠ‚ AG(2;F,54P) [i] based on
  1. linear OOA(8⁹⁵, 64, F₈, 2, 81) (dual of [(64, 2), 33, 82]-NRT-code), using algebraic-geometric NRT-code AG(2;F,46P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁸⁷, 64, F₈, 2, 73) (dual of [(64, 2), 41, 74]-NRT-code), using algebraic-geometric NRT-code AG(2;F,54P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁷, 7, F₈, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 2, 7) (dual of [(8, 2), 9, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;9,8) [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.