MinT - Information on Result #2638814

Information on Result #2638814

Linear OOA(4²⁵⁶, 154, F₄, 3, 108) (dual of [(154, 3), 206, 109]-NRT-code), using strength reduction based on linear OOA(4²⁵⁶, 154, F₄, 3, 109) (dual of [(154, 3), 206, 110]-NRT-code), using

constructionÂ X applied to AG(3;F,277P) âŠ‚ AG(3;F,310P) [i] based on
1. linear OOA(4²¹⁴, 129, F₄, 3, 109) (dual of [(129, 3), 173, 110]-NRT-code), using algebraic-geometric NRT-code AG(3;F,277P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁸¹, 129, F₄, 3, 76) (dual of [(129, 3), 206, 77]-NRT-code), using algebraic-geometric NRT-code AG(3;F,310P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130 (see above)
3. linear OOA(4⁴², 25, F₄, 3, 32) (dual of [(25, 3), 33, 33]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴², 26, F₄, 3, 32) (dual of [(26, 3), 36, 33]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,45P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, 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.