MinT - Information on Result #671928

Information on Result #671928

Linear OA(3²¹⁰, 217, F₃, 134) (dual of [217, 7, 135]-code), using juxtaposition based on

linear OA(3⁴², 49, F₃, 26) (dual of [49, 7, 27]-code), using
- constructionÂ XX applied to C₁, D₂, C₂ = C₁Â âˆ©Â D₂, and D₁ = C₁Â +Â D₂ [i] based on
  1. linear OA(3³⁴, 40, F₃, 23) (dual of [40, 6, 24]-code), using code C₁ for uÂ =Â 4 by de Boer and Brouwer [i]
  2. linear OA(3³⁷, 40, F₃, 24) (dual of [40, 3, 25]-code), using augmented code D₂ for uÂ =Â 4 by de Boer and Brouwer [i]
  3. linear OA(3³⁸, 40, F₃, 29) (dual of [40, 2, 30]-code), using code C₂ for uÂ =Â 4 by de Boer and Brouwer [i]
  4. linear OA(3³³, 40, F₃, 21) (dual of [40, 7, 22]-code), using augmented code D₁ for uÂ =Â 4 by de Boer and Brouwer [i]
  5. linear OA(3¹, 2, F₃, 1) (dual of [2, 1, 2]-code), using
    - dual of repetition code with length 2 [i]
  6. linear OA(3³, 7, F₃, 2) (dual of [7, 4, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
      - Hamming code H(3,3) [i]
linear OA(3¹⁶¹, 168, F₃, 107) (dual of [168, 7, 108]-code), using
- (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
  1. linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
      2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]
  2. linear OA(3⁵⁵, 56, F₃, 53) (dual of [56, 1, 54]-code), using
    - strength reduction [i] based on linear OA(3⁵⁵, 56, F₃, 55) (dual of [56, 1, 56]-code or 56-arc in PG(54,3)), using
      - dual of repetition code with length 56 [i]
  3. linear OA(3⁵⁶, 56, F₃, 56) (dual of [56, 0, 57]-code or 56-arc in PG(55,3)), using
    - complete OA / dual of code with only one code word [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.