MinT - Information on Result #846172

Information on Result #846172

Linear OOA(8⁶⁸, 45, F₈, 2, 40) (dual of [(45, 2), 22, 41]-NRT-code), using OOA 2-folding based on linear OA(8⁶⁸, 90, F₈, 40) (dual of [90, 22, 41]-code), using

constructionÂ X applied to AG(F,23P) âŠ‚ AG(F,35P) [i] based on
1. linear OA(8⁵³, 64, F₈, 41) (dual of [64, 11, 42]-code), using algebraic-geometric code AG(F,23P) with known gap numbers [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 OA(8⁴², 64, F₈, 28) (dual of [64, 22, 29]-code), using algebraic-geometric code AG(F,35P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OA(8¹⁵, 26, F₈, 11) (dual of [26, 11, 12]-code), using
  - constructionÂ X applied to AG(F,11P) âŠ‚ AG(F,13P) [i] based on
    1. linear OA(8¹⁴, 23, F₈, 11) (dual of [23, 9, 12]-code), using algebraic-geometric code AG(F,11P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]
    2. linear OA(8¹², 23, F₈, 9) (dual of [23, 11, 10]-code), using algebraic-geometric code AG(F,13P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24 (see above)
    3. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.