MinT - Information on Result #2633251

Information on Result #2633251

Linear OOA(4¹⁷⁹, 77, F₄, 3, 110) (dual of [(77, 3), 52, 111]-NRT-code), using strength reduction based on linear OOA(4¹⁷⁹, 77, F₄, 3, 111) (dual of [(77, 3), 52, 112]-NRT-code), using

constructionÂ X applied to AG(3;F,83P) âŠ‚ AG(3;F,100P) [i] based on
1. linear OOA(4¹⁶⁰, 65, F₄, 3, 111) (dual of [(65, 3), 35, 112]-NRT-code), using algebraic-geometric NRT-code AG(3;F,83P) [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(4¹⁴³, 65, F₄, 3, 94) (dual of [(65, 3), 52, 95]-NRT-code), using algebraic-geometric NRT-code AG(3;F,100P) [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.