MinT - Information on Result #671920

Information on Result #671920

Linear OA(3¹⁹⁸, 205, F₃, 126) (dual of [205, 7, 127]-code), using juxtaposition based on

linear OA(3³⁰, 37, F₃, 18) (dual of [37, 7, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3³⁰, 38, F₃, 18) (dual of [38, 8, 19]-code), using
  - 2 times truncation [i] based on linear OA(3³², 40, F₃, 20) (dual of [40, 8, 21]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(9⁶, 10, F₉, 6) (dual of [10, 4, 7]-code or 10-arc in PG(5,9)), using
        extended Reedâ€“Solomon code RS_e(4,9) [i]
      2. linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
        extended Reedâ€“Solomon code RS_e(2,3) [i]
        Hamming code H(2,3) [i]
        Simplex code S(2,3) [i]
        the Tetracode [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁹⁸, 41, F₃, 5, 126) (dual of [(41, 5), 7, 127]-NRT-code)	[i]		OOA Folding