MinT - Information on Result #941398

Information on Result #941398

Linear OOA(8¹⁶⁷, 140, F₈, 2, 85) (dual of [(140, 2), 113, 86]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶², 70, F₈, 2, 42) (dual of [(70, 2), 78, 43]-NRT-code), using
- constructionÂ X applied to AG(2;F,85P) âŠ‚ AG(2;F,92P) [i] based on
  1. linear OOA(8⁵⁶, 64, F₈, 2, 42) (dual of [(64, 2), 72, 43]-NRT-code), using algebraic-geometric NRT-code AG(2;F,85P) [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(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 (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(8¹⁰⁵, 70, F₈, 2, 85) (dual of [(70, 2), 35, 86]-NRT-code), using
- constructionÂ X applied to AG(2;F,42P) âŠ‚ AG(2;F,49P) [i] based on
  1. linear OOA(8⁹⁹, 64, F₈, 2, 85) (dual of [(64, 2), 29, 86]-NRT-code), using algebraic-geometric NRT-code AG(2;F,42P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁹², 64, F₈, 2, 78) (dual of [(64, 2), 36, 79]-NRT-code), using algebraic-geometric NRT-code AG(2;F,49P) [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) (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.