MinT - Information on Result #2638905

Information on Result #2638905

Linear OOA(4²⁵⁷, 141, F₄, 3, 132) (dual of [(141, 3), 166, 133]-NRT-code), using strength reduction based on linear OOA(4²⁵⁷, 141, F₄, 3, 133) (dual of [(141, 3), 166, 134]-NRT-code), using

constructionÂ X applied to AG(3;F,253P) âŠ‚ AG(3;F,270P) [i] based on
1. linear OOA(4²³⁸, 129, F₄, 3, 133) (dual of [(129, 3), 149, 134]-NRT-code), using algebraic-geometric NRT-code AG(3;F,253P) [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(4²²¹, 129, F₄, 3, 116) (dual of [(129, 3), 166, 117]-NRT-code), using algebraic-geometric NRT-code AG(3;F,270P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130 (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.