MinT - Information on Result #626279

Information on Result #626279

Linear OA(8¹²¹, 126, F₈, 99) (dual of [126, 5, 100]-code), using repeating each code word 2 times based on linear OA(8⁵⁸, 63, F₈, 49) (dual of [63, 5, 50]-code), using

2 times truncation [i] based on linear OA(8⁶⁰, 65, F₈, 51) (dual of [65, 5, 52]-code), using
- constructionÂ X applied to AG(F,12P) âŠ‚ AG(F,13P) [i] based on
  1. linear OA(8⁶⁰, 64, F₈, 51) (dual of [64, 4, 52]-code), using algebraic-geometric code AG(F,12P) 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(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [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.