MinT - Information on Result #2267242

Information on Result #2267242

Linear OA(3¹³⁰, 193, F₃, 50) (dual of [193, 63, 51]-code), using 2 times code embedding in larger space based on linear OA(3¹²⁸, 191, F₃, 50) (dual of [191, 63, 51]-code), using

1 times truncation [i] based on linear OA(3¹²⁹, 192, F₃, 51) (dual of [192, 63, 52]-code), using
- concatenation of two codes [i] based on
  1. linear OA(27²⁷, 48, F₂₇, 25) (dual of [48, 21, 26]-code), using
    - extended algebraic-geometric code AG_e(F,22P) [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]
  2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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.

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

Other Results with Identical Parameters

None.

Depending Results

None.