MinT - Information on Result #2499103

Information on Result #2499103

Linear OOA(4¹³¹, 138, F₄, 2, 54) (dual of [(138, 2), 145, 55]-NRT-code), using 4¹ times duplication based on linear OOA(4¹³⁰, 138, F₄, 2, 54) (dual of [(138, 2), 146, 55]-NRT-code), using

trace code [i] based on linear OOA(16⁶⁵, 69, F₁₆, 2, 54) (dual of [(69, 2), 73, 55]-NRT-code), using
- constructionÂ X applied to AG(2;F,73P) âŠ‚ AG(2;F,79P) [i] based on
  1. linear OOA(16⁶⁰, 64, F₁₆, 2, 54) (dual of [(64, 2), 68, 55]-NRT-code), using algebraic-geometric NRT-code AG(2;F,73P) [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(16⁵⁴, 64, F₁₆, 2, 48) (dual of [(64, 2), 74, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,79P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16⁵, 5, F₁₆, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁵, 16, F₁₆, 2, 5) (dual of [(16, 2), 27, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;27,16) [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.