MinT - Information on Result #2500446

Information on Result #2500446

Linear OOA(4¹⁵⁹, 136, F₄, 2, 69) (dual of [(136, 2), 113, 70]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁵⁸, 136, F₄, 2, 69) (dual of [(136, 2), 114, 70]-NRT-code), using

trace code [i] based on linear OOA(16⁷⁹, 68, F₁₆, 2, 69) (dual of [(68, 2), 57, 70]-NRT-code), using
- constructionÂ X applied to AG(2;F,58P) âŠ‚ AG(2;F,63P) [i] based on
  1. linear OOA(16⁷⁵, 64, F₁₆, 2, 69) (dual of [(64, 2), 53, 70]-NRT-code), using algebraic-geometric NRT-code AG(2;F,58P) [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(16⁷⁰, 64, F₁₆, 2, 64) (dual of [(64, 2), 58, 65]-NRT-code), using algebraic-geometric NRT-code AG(2;F,63P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16⁴, 4, F₁₆, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁴, 16, F₁₆, 2, 4) (dual of [(16, 2), 28, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;28,16) [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.