MinT - Information on Result #2499307

Information on Result #2499307

Linear OOA(4¹⁵³, 156, F₄, 2, 56) (dual of [(156, 2), 159, 57]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁵², 156, F₄, 2, 56) (dual of [(156, 2), 160, 57]-NRT-code), using

trace code [i] based on linear OOA(16⁷⁶, 78, F₁₆, 2, 56) (dual of [(78, 2), 80, 57]-NRT-code), using
- constructionÂ X applied to AG(2;F,71P) âŠ‚ AG(2;F,86P) [i] based on
  1. linear OOA(16⁶², 64, F₁₆, 2, 56) (dual of [(64, 2), 66, 57]-NRT-code), using algebraic-geometric NRT-code AG(2;F,71P) [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(16⁴⁷, 64, F₁₆, 2, 41) (dual of [(64, 2), 81, 42]-NRT-code), using algebraic-geometric NRT-code AG(2;F,86P) [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.