MinT - Information on Result #2637577

Information on Result #2637577

Linear OOA(4²⁴², 138, F₄, 3, 122) (dual of [(138, 3), 172, 123]-NRT-code), using strength reduction based on linear OOA(4²⁴², 138, F₄, 3, 123) (dual of [(138, 3), 172, 124]-NRT-code), using

constructionÂ X applied to AG(3;F,263P) âŠ‚ AG(3;F,277P) [i] based on
1. linear OOA(4²²⁸, 129, F₄, 3, 123) (dual of [(129, 3), 159, 124]-NRT-code), using algebraic-geometric NRT-code AG(3;F,263P) [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(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 (see above)
3. linear OOA(4¹⁴, 9, F₄, 3, 13) (dual of [(9, 3), 13, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [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.