MinT - Information on Result #2498318

Information on Result #2498318

Linear OOA(4¹¹⁷, 140, F₄, 2, 46) (dual of [(140, 2), 163, 47]-NRT-code), using 4¹ times duplication based on linear OOA(4¹¹⁶, 140, F₄, 2, 46) (dual of [(140, 2), 164, 47]-NRT-code), using

trace code [i] based on linear OOA(16⁵⁸, 70, F₁₆, 2, 46) (dual of [(70, 2), 82, 47]-NRT-code), using
- constructionÂ X applied to AG(2;F,81P) âŠ‚ AG(2;F,88P) [i] based on
  1. linear OOA(16⁵², 64, F₁₆, 2, 46) (dual of [(64, 2), 76, 47]-NRT-code), using algebraic-geometric NRT-code AG(2;F,81P) [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(16⁴⁵, 64, F₁₆, 2, 39) (dual of [(64, 2), 83, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,88P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16⁶, 6, F₁₆, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁶, 16, F₁₆, 2, 6) (dual of [(16, 2), 26, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;26,16) [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.