MinT - Information on Result #2693888

Information on Result #2693888

Linear OOA(4²⁵⁰, 157, F₄, 3, 97) (dual of [(157, 3), 221, 98]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²⁴⁷, 156, F₄, 3, 97) (dual of [(156, 3), 221, 98]-NRT-code), using

constructionÂ X applied to AG(3;F,289P) âŠ‚ AG(3;F,325P) [i] based on
1. linear OOA(4²⁰², 129, F₄, 3, 97) (dual of [(129, 3), 185, 98]-NRT-code), using algebraic-geometric NRT-code AG(3;F,289P) [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(4¹⁶⁶, 129, F₄, 3, 61) (dual of [(129, 3), 221, 62]-NRT-code), using algebraic-geometric NRT-code AG(3;F,325P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130 (see above)
3. linear OOA(4⁴⁵, 27, F₄, 3, 35) (dual of [(27, 3), 36, 36]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(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.