MinT - Information on Result #2489431

Information on Result #2489431

Linear OOA(3¹⁶⁷, 172, F₃, 2, 53) (dual of [(172, 2), 177, 54]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁶⁶, 172, F₃, 2, 53) (dual of [(172, 2), 178, 54]-NRT-code), using

trace code [i] based on linear OOA(9⁸³, 86, F₉, 2, 53) (dual of [(86, 2), 89, 54]-NRT-code), using
- constructionÂ X applied to AG(2;F,92P) âŠ‚ AG(2;F,105P) [i] based on
  1. linear OOA(9⁷⁰, 73, F₉, 2, 53) (dual of [(73, 2), 76, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,92P) [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(9⁵⁷, 73, F₉, 2, 40) (dual of [(73, 2), 89, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,105P) [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.