MinT - Information on Result #941370

Information on Result #941370

Linear OOA(8¹⁶¹, 135, F₈, 2, 84) (dual of [(135, 2), 109, 85]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵⁹, 67, F₈, 2, 42) (dual of [(67, 2), 75, 43]-NRT-code), using
- constructionÂ X applied to AG(2;F,85P) âŠ‚ AG(2;F,89P) [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(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 (see above)
  3. linear OOA(8³, 3, F₈, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8³, 8, F₈, 2, 3) (dual of [(8, 2), 13, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;13,8) [i]
linear OOA(8¹⁰², 68, F₈, 2, 84) (dual of [(68, 2), 34, 85]-NRT-code), using
- constructionÂ X applied to AG(2;F,43P) âŠ‚ AG(2;F,48P) [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(8⁹³, 64, F₈, 2, 79) (dual of [(64, 2), 35, 80]-NRT-code), using algebraic-geometric NRT-code AG(2;F,48P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OOA(8⁴, 4, F₈, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 2, 4) (dual of [(8, 2), 12, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;12,8) [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.