MinT - Information on Result #941225

Information on Result #941225

Linear OOA(8¹⁵³, 139, F₈, 2, 76) (dual of [(139, 2), 125, 77]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵⁷, 69, F₈, 2, 38) (dual of [(69, 2), 81, 39]-NRT-code), using
- constructionÂ X applied to AG(2;F,89P) âŠ‚ AG(2;F,95P) [i] based on
  1. linear OOA(8⁵², 64, F₈, 2, 38) (dual of [(64, 2), 76, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,89P) [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(8⁴⁶, 64, F₈, 2, 32) (dual of [(64, 2), 82, 33]-NRT-code), using algebraic-geometric NRT-code AG(2;F,95P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁵, 5, F₈, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁵, 8, F₈, 2, 5) (dual of [(8, 2), 11, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;11,8) [i]
linear OOA(8⁹⁶, 70, F₈, 2, 76) (dual of [(70, 2), 44, 77]-NRT-code), using
- constructionÂ X applied to AG(2;F,51P) âŠ‚ AG(2;F,58P) [i] based on
  1. 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)
  2. linear OOA(8⁸³, 64, F₈, 2, 69) (dual of [(64, 2), 45, 70]-NRT-code), using algebraic-geometric NRT-code AG(2;F,58P) [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]

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.