MinT - Information on Result #818723

Information on Result #818723

Linear OOA(3¹⁸⁹, 172, F₃, 2, 61) (dual of [(172, 2), 155, 62]-NRT-code), using OOA 2-folding based on linear OA(3¹⁸⁹, 344, F₃, 61) (dual of [344, 155, 62]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁸⁹, 345, F₃, 61) (dual of [345, 156, 62]-code), using
- concatenation of two codes [i] based on
  1. linear OA(81³⁰, 69, F₈₁, 30) (dual of [69, 39, 31]-code or 69-arc in PG(29,81)), using
    - discarding factors / shortening the dual code based on linear OA(81³⁰, 81, F₈₁, 30) (dual of [81, 51, 31]-code or 81-arc in PG(29,81)), using
      - Reedâ€“Solomon code RS(51,81) [i]
  2. linear OA(3¹, 5, F₃, 1) (dual of [5, 4, 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.

Other Results with Identical Parameters

None.

Depending Results

None.