MinT - Information on Result #731750

Information on Result #731750

Linear OA(3¹⁹², 199, F₃, 124) (dual of [199, 7, 125]-code), using juxtaposition based on

linear OA(3²⁴, 31, F₃, 16) (dual of [31, 7, 17]-code), using
- constructionÂ XX applied to C₁Â =Â C([0,27]), C₂Â =Â C([1,33]), C₃Â =Â C₁Â +Â C₂Â =Â C([1,27]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([0,33]) [i] based on
  1. linear OA(3²⁰, 26, F₃, 14) (dual of [26, 6, 15]-code), using contraction [i] based on linear OA(3⁴⁶, 52, F₃, 29) (dual of [52, 6, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 52Â | 3⁶âˆ’1, defining interval IÂ =Â [0,27], and minimum distance dÂ â‰¥ |{−1,0,…,27}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(3²², 26, F₃, 16) (dual of [26, 4, 17]-code), using contraction [i] based on linear OA(3⁴⁸, 52, F₃, 33) (dual of [52, 4, 34]-code), using the narrow-sense BCH-code C(I) with length 52Â | 3⁶âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
  3. linear OA(3²³, 26, F₃, 17) (dual of [26, 3, 18]-code), using contraction [i] based on linear OA(3⁴⁹, 52, F₃, 35) (dual of [52, 3, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 52Â | 3⁶âˆ’1, defining interval IÂ =Â [0,33], and minimum distance dÂ â‰¥ |{−1,0,…,33}|+1Â =Â 36 (BCH-bound) [i]
  4. linear OA(3¹⁹, 26, F₃, 13) (dual of [26, 7, 14]-code), using contraction [i] based on linear OA(3⁴⁵, 52, F₃, 27) (dual of [52, 7, 28]-code), using the narrow-sense BCH-code C(I) with length 52Â | 3⁶âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
  5. linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
    - dual of repetition code with length 1 [i]
  6. 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]
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.