MinT - Information on Result #2638438

Information on Result #2638438

Linear OOA(4²⁵², 117, F₄, 3, 156) (dual of [(117, 3), 99, 157]-NRT-code), using strength reduction based on linear OOA(4²⁵², 117, F₄, 3, 157) (dual of [(117, 3), 99, 158]-NRT-code), using

constructionÂ X applied to AG(3;F,151P) âŠ‚ AG(3;F,171P) [i] based on
1. linear OOA(4²³⁰, 103, F₄, 3, 157) (dual of [(103, 3), 79, 158]-NRT-code), using algebraic-geometric NRT-code AG(3;F,151P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4²¹⁰, 103, F₄, 3, 137) (dual of [(103, 3), 99, 138]-NRT-code), using algebraic-geometric NRT-code AG(3;F,171P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104 (see above)
3. linear OOA(4²², 14, F₄, 3, 19) (dual of [(14, 3), 20, 20]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,22P) [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.