MinT - Information on Result #2632277

Information on Result #2632277

Linear OOA(4¹⁵⁸, 77, F₄, 3, 89) (dual of [(77, 3), 73, 90]-NRT-code), using strength reduction based on linear OOA(4¹⁵⁸, 77, F₄, 3, 90) (dual of [(77, 3), 73, 91]-NRT-code), using

constructionÂ X applied to AG(3;F,104P) âŠ‚ AG(3;F,121P) [i] based on
1. linear OOA(4¹³⁹, 65, F₄, 3, 90) (dual of [(65, 3), 56, 91]-NRT-code), using algebraic-geometric NRT-code AG(3;F,104P) [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
  - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹²², 65, F₄, 3, 73) (dual of [(65, 3), 73, 74]-NRT-code), using algebraic-geometric NRT-code AG(3;F,121P) [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66 (see above)
3. linear OOA(4¹⁹, 12, F₄, 3, 16) (dual of [(12, 3), 17, 17]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹⁹, 14, F₄, 3, 16) (dual of [(14, 3), 23, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,25P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [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.