MinT - Information on Result #2449798

Information on Result #2449798

Linear OOA(8⁷⁸, 78, F₈, 2, 49) (dual of [(78, 2), 78, 50]-NRT-code), using strength reduction based on linear OOA(8⁷⁸, 78, F₈, 2, 50) (dual of [(78, 2), 78, 51]-NRT-code), using

constructionÂ X applied to AG(2;F,77P) âŠ‚ AG(2;F,91P) [i] based on
1. linear OOA(8⁶⁴, 64, F₈, 2, 50) (dual of [(64, 2), 64, 51]-NRT-code), using algebraic-geometric NRT-code AG(2;F,77P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
  - the Suzuki function field over F₈ [i]
2. linear OOA(8⁵⁰, 64, F₈, 2, 36) (dual of [(64, 2), 78, 37]-NRT-code), using algebraic-geometric NRT-code AG(2;F,91P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹⁴, 14, F₈, 2, 13) (dual of [(14, 2), 14, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,14P) [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.