MinT - Information on Result #2500798

Information on Result #2500798

Linear OOA(4¹⁷⁵, 142, F₄, 2, 74) (dual of [(142, 2), 109, 75]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁷⁴, 142, F₄, 2, 74) (dual of [(142, 2), 110, 75]-NRT-code), using

trace code [i] based on linear OOA(16⁸⁷, 71, F₁₆, 2, 74) (dual of [(71, 2), 55, 75]-NRT-code), using
- constructionÂ X applied to AG(2;F,53P) âŠ‚ AG(2;F,61P) [i] based on
  1. linear OOA(16⁸⁰, 64, F₁₆, 2, 74) (dual of [(64, 2), 48, 75]-NRT-code), using algebraic-geometric NRT-code AG(2;F,53P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
  2. linear OOA(16⁷², 64, F₁₆, 2, 66) (dual of [(64, 2), 56, 67]-NRT-code), using algebraic-geometric NRT-code AG(2;F,61P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16⁷, 7, F₁₆, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁷, 16, F₁₆, 2, 7) (dual of [(16, 2), 25, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;25,16) [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.