MinT - Information on Result #2645795

Information on Result #2645795

Linear OOA(8¹⁶¹, 111, F₈, 3, 102) (dual of [(111, 3), 172, 103]-NRT-code), using strength reduction based on linear OOA(8¹⁶¹, 111, F₈, 3, 103) (dual of [(111, 3), 172, 104]-NRT-code), using

constructionÂ X applied to AG(3;F,187P) âŠ‚ AG(3;F,208P) [i] based on
1. linear OOA(8¹⁴⁰, 97, F₈, 3, 103) (dual of [(97, 3), 151, 104]-NRT-code), using algebraic-geometric NRT-code AG(3;F,187P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
  - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. linear OOA(8¹¹⁹, 97, F₈, 3, 82) (dual of [(97, 3), 172, 83]-NRT-code), using algebraic-geometric NRT-code AG(3;F,208P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
3. linear OOA(8²¹, 14, F₈, 3, 20) (dual of [(14, 3), 21, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [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.