MinT - Information on Result #2499963

Information on Result #2499963

Linear OOA(4¹⁵⁷, 146, F₄, 2, 63) (dual of [(146, 2), 135, 64]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁵⁶, 146, F₄, 2, 63) (dual of [(146, 2), 136, 64]-NRT-code), using

trace code [i] based on linear OOA(16⁷⁸, 73, F₁₆, 2, 63) (dual of [(73, 2), 68, 64]-NRT-code), using
- constructionÂ X applied to AG(2;F,64P) âŠ‚ AG(2;F,74P) [i] based on
  1. linear OOA(16⁶⁹, 64, F₁₆, 2, 63) (dual of [(64, 2), 59, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,64P) [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(16⁵⁹, 64, F₁₆, 2, 53) (dual of [(64, 2), 69, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,74P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16⁹, 9, F₁₆, 2, 9) (dual of [(9, 2), 9, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁹, 16, F₁₆, 2, 9) (dual of [(16, 2), 23, 10]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;23,16) [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.