MinT - Information on Result #2489695

Information on Result #2489695

Linear OOA(3¹⁷³, 172, F₃, 2, 56) (dual of [(172, 2), 171, 57]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁷², 172, F₃, 2, 56) (dual of [(172, 2), 172, 57]-NRT-code), using

trace code [i] based on linear OOA(9⁸⁶, 86, F₉, 2, 56) (dual of [(86, 2), 86, 57]-NRT-code), using
- constructionÂ X applied to AG(2;F,89P) âŠ‚ AG(2;F,102P) [i] based on
  1. linear OOA(9⁷³, 73, F₉, 2, 56) (dual of [(73, 2), 73, 57]-NRT-code), using algebraic-geometric NRT-code AG(2;F,89P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(9⁶⁰, 73, F₉, 2, 43) (dual of [(73, 2), 86, 44]-NRT-code), using algebraic-geometric NRT-code AG(2;F,102P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74 (see above)
  3. linear OOA(9¹³, 13, F₉, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹³, 16, F₉, 2, 12) (dual of [(16, 2), 19, 13]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [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.