MinT - Information on Result #2634024

Information on Result #2634024

Linear OOA(4¹⁹⁴, 72, F₄, 3, 135) (dual of [(72, 3), 22, 136]-NRT-code), using strength reduction based on linear OOA(4¹⁹⁴, 72, F₄, 3, 136) (dual of [(72, 3), 22, 137]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,54P) [i] based on
1. linear OOA(4¹⁶⁴, 55, F₄, 3, 164) (dual of [(55, 3), 1, 165]-NRT-code), using algebraic-geometric NRT-code AG(3;F,0P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁴³, 55, F₄, 3, 110) (dual of [(55, 3), 22, 111]-NRT-code), using algebraic-geometric NRT-code AG(3;F,54P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
3. linear OOA(4³⁰, 17, F₄, 3, 25) (dual of [(17, 3), 21, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,25P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, 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.