MinT - Information on Result #661611

Information on Result #661611

Linear OA(8⁹¹, 96, F₈, 73) (dual of [96, 5, 74]-code), using juxtaposition based on

linear OA(8²¹, 26, F₈, 17) (dual of [26, 5, 18]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,7P) [i] based on
  1. linear OA(8²⁰, 23, F₈, 17) (dual of [23, 3, 18]-code), using algebraic-geometric code AG(F,5P) [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(8¹⁸, 23, F₈, 15) (dual of [23, 5, 16]-code), using algebraic-geometric code AG(F,7P) [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]
linear OA(8⁶⁵, 70, F₈, 55) (dual of [70, 5, 56]-code), using
- constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,13P) [i] based on
  1. linear OA(8⁶¹, 64, F₈, 55) (dual of [64, 3, 56]-code), using algebraic-geometric code AG(F,10P) 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(8⁵⁹, 64, F₈, 50) (dual of [64, 5, 51]-code), using algebraic-geometric code AG(F,13P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
  3. linear OA(8⁴, 6, F₈, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,8)), using
    - discarding factors / shortening the dual code based on linear OA(8⁴, 8, F₈, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
      - Reedâ€“Solomon code RS(4,8) [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.