MinT - Information on Result #2693131

Information on Result #2693131

Linear OOA(4²²², 167, F₄, 3, 75) (dual of [(167, 3), 279, 76]-NRT-code), using 4¹ times duplication based on linear OOA(4²²¹, 167, F₄, 3, 75) (dual of [(167, 3), 280, 76]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁵⁹, 37, F₄, 3, 37) (dual of [(37, 3), 52, 38]-NRT-code), using
  - constructionÂ X applied to AG(3;F,58P) âŠ‚ AG(3;F,66P) [i] based on
    1. linear OOA(4⁵², 32, F₄, 3, 37) (dual of [(32, 3), 44, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,58P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
    2. linear OOA(4⁴⁴, 32, F₄, 3, 29) (dual of [(32, 3), 52, 30]-NRT-code), using algebraic-geometric NRT-code AG(3;F,66P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
    3. linear OOA(4⁷, 5, F₄, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;8,4) [i]
2. linear OOA(4¹⁶², 130, F₄, 3, 75) (dual of [(130, 3), 228, 76]-NRT-code), using
  - extracting embedded OOA [i] based on digital (87, 162, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 81, 65)-net over F₁₆, using
      - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [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.