MinT - Information on Result #700850

Information on Result #700850

Linear OA(3⁶⁹, 144, F₃, 22) (dual of [144, 75, 23]-code), using constructionÂ X applied to C({0,1,2,4,5,7,8,10,11,13,40,67,76}) âŠ‚ C([0,13]) based on

linear OA(3⁶¹, 121, F₃, 22) (dual of [121, 60, 23]-code), using the cyclic code C(A) with length 121Â | 3⁵âˆ’1, defining set AÂ =Â {0,1,2,4,5,7,8,10,11,13,40,67,76}, and minimum distance dÂ â‰¥ |{−6,−5,…,15}|+1Â =Â 23 (BCH-bound) [i]
linear OA(3⁴⁶, 121, F₃, 16) (dual of [121, 75, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 121Â | 3⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
linear OA(3⁸, 23, F₃, 5) (dual of [23, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁸, 26, F₃, 5) (dual of [26, 18, 6]-code), using
  - dual code (with bound on d by constructionÂ Y1) [i] based on
    1. linear OA(3¹⁸, 26, F₃, 12) (dual of [26, 8, 13]-code), using
      - 2 times truncation [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]
    2. nonexistence of linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), because
      - â€œHNâ€ bound on codes from Brouwerâ€™s database [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.