MinT - Information on Result #2644677

Information on Result #2644677

Linear OOA(8¹²⁹, 132, F₈, 3, 64) (dual of [(132, 3), 267, 65]-NRT-code), using strength reduction based on linear OOA(8¹²⁹, 132, F₈, 3, 65) (dual of [(132, 3), 267, 66]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8⁴⁶, 65, F₈, 3, 32) (dual of [(65, 3), 149, 33]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,162P) [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(8⁸³, 67, F₈, 3, 65) (dual of [(67, 3), 118, 66]-NRT-code), using
  - constructionÂ X applied to AG(3;F,126P) âŠ‚ AG(3;F,131P) [i] based on
    1. linear OOA(8⁷⁹, 64, F₈, 3, 65) (dual of [(64, 3), 113, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,126P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    2. linear OOA(8⁷⁴, 64, F₈, 3, 60) (dual of [(64, 3), 118, 61]-NRT-code), using algebraic-geometric NRT-code AG(3;F,131P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    3. linear OOA(8⁴, 3, F₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;20,8) [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.