MinT - Information on Result #941380

Information on Result #941380

Linear OOA(8¹⁶⁸, 142, F₈, 2, 84) (dual of [(142, 2), 116, 85]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁶³, 71, F₈, 2, 42) (dual of [(71, 2), 79, 43]-NRT-code), using
- constructionÂ X applied to AG(2;F,85P) âŠ‚ AG(2;F,93P) [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(8⁴⁸, 64, F₈, 2, 34) (dual of [(64, 2), 80, 35]-NRT-code), using algebraic-geometric NRT-code AG(2;F,93P) [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]
linear OOA(8¹⁰⁵, 71, F₈, 2, 84) (dual of [(71, 2), 37, 85]-NRT-code), using
- constructionÂ X applied to AG(2;F,43P) âŠ‚ AG(2;F,51P) [i] based on
  1. linear OOA(8⁹⁸, 64, F₈, 2, 84) (dual of [(64, 2), 30, 85]-NRT-code), using algebraic-geometric NRT-code AG(2;F,43P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  2. linear OOA(8⁹⁰, 64, F₈, 2, 76) (dual of [(64, 2), 38, 77]-NRT-code), using algebraic-geometric NRT-code AG(2;F,51P) [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) (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.