MinT - Information on Result #2624672

Information on Result #2624672

Linear OOA(3¹⁷⁷, 66, F₃, 3, 111) (dual of [(66, 3), 21, 112]-NRT-code), using strength reduction based on linear OOA(3¹⁷⁷, 66, F₃, 3, 113) (dual of [(66, 3), 21, 114]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁶³, 28, F₃, 3, 48) (dual of [(28, 3), 21, 49]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,35P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁹³, 38, F₃, 3, 64) (dual of [(38, 3), 21, 65]-NRT-code), using
  - constructionÂ X applied to AG(3;F,21P) âŠ‚ AG(3;F,23P) [i] based on
    1. linear OOA(3⁹¹, 36, F₃, 3, 65) (dual of [(36, 3), 17, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,21P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
    2. linear OOA(3⁸⁷, 36, F₃, 3, 61) (dual of [(36, 3), 21, 62]-NRT-code), using algebraic-geometric NRT-code AG(3;F,23P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    3. linear OOA(3², 2, F₃, 3, 2) (dual of [(2, 3), 4, 3]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3², 3, F₃, 3, 2) (dual of [(3, 3), 7, 3]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;7,3) [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.