MinT - Information on Result #982466

Information on Result #982466

Linear OOA(8⁸⁶, 34, F₈, 3, 68) (dual of [(34, 3), 16, 69]-NRT-code), using OOA 2-folding based on linear OOA(8⁸⁶, 68, F₈, 2, 68) (dual of [(68, 2), 50, 69]-NRT-code), using

constructionÂ X applied to AG(2;F,59P) âŠ‚ AG(2;F,64P) [i] based on
1. linear OOA(8⁸², 64, F₈, 2, 68) (dual of [(64, 2), 46, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,59P) [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(8⁷⁷, 64, F₈, 2, 63) (dual of [(64, 2), 51, 64]-NRT-code), using algebraic-geometric NRT-code AG(2;F,64P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8⁴, 4, F₈, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 2, 4) (dual of [(8, 2), 12, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;12,8) [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.