MinT - Information on Result #675059

Information on Result #675059

Linear OA(3¹⁵³, 19712, F₃, 25) (dual of [19712, 19559, 26]-code), using constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) based on

linear OA(3¹⁴⁵, 19684, F₃, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
linear OA(3¹⁰⁹, 19684, F₃, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
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
  1. 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(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]

Mode: Constructive and linear.

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