MinT - Information on Result #2498822

Information on Result #2498822

Linear OOA(4¹⁴³, 156, F₄, 2, 51) (dual of [(156, 2), 169, 52]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁴², 156, F₄, 2, 51) (dual of [(156, 2), 170, 52]-NRT-code), using

trace code [i] based on linear OOA(16⁷¹, 78, F₁₆, 2, 51) (dual of [(78, 2), 85, 52]-NRT-code), using
- constructionÂ X applied to AG(2;F,76P) âŠ‚ AG(2;F,91P) [i] based on
  1. linear OOA(16⁵⁷, 64, F₁₆, 2, 51) (dual of [(64, 2), 71, 52]-NRT-code), using algebraic-geometric NRT-code AG(2;F,76P) [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(16⁴², 64, F₁₆, 2, 36) (dual of [(64, 2), 86, 37]-NRT-code), using algebraic-geometric NRT-code AG(2;F,91P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16¹⁴, 14, F₁₆, 2, 14) (dual of [(14, 2), 14, 15]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16¹⁴, 16, F₁₆, 2, 14) (dual of [(16, 2), 18, 15]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;18,16) [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.