MinT - Information on Result #662052

Information on Result #662052

Linear OA(3³³, 90, F₃, 11) (dual of [90, 57, 12]-code), using (u,Â u+v)-construction based on

linear OA(3¹², 45, F₃, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹², 54, F₃, 5) (dual of [54, 42, 6]-code), using
  - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
    1. linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 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]
    2. linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
      - Hamming code H(3,3) [i]
    3. linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
      - dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
        nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
        2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
linear OA(3²¹, 45, F₃, 11) (dual of [45, 24, 12]-code), using
- 3 times truncation [i] based on linear OA(3²⁴, 48, F₃, 14) (dual of [48, 24, 15]-code), using
  - extended quadratic residue code Q_e(48,3) [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.