MinT - Information on Result #641267

Information on Result #641267

Linear OA(7⁷⁷, 82, F₇, 59) (dual of [82, 5, 60]-code), using juxtaposition based on

linear OA(7²¹, 26, F₇, 17) (dual of [26, 5, 18]-code), using
- constructionÂ X applied to C([0,8]) âŠ‚ C([1,8]) [i] based on
  1. linear OA(7²¹, 25, F₇, 17) (dual of [25, 4, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 25Â | 7⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  2. linear OA(7²⁰, 25, F₇, 16) (dual of [25, 5, 17]-code), using the narrow-sense BCH-code C(I) with length 25Â | 7⁴âˆ’1, defining interval IÂ =Â [1,8], and minimum distance dÂ â‰¥ |{−10,−7,−4,…,10}|+1Â =Â 17 (BCH-bound) [i]
  3. linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
linear OA(7⁵¹, 56, F₇, 41) (dual of [56, 5, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁵¹, 57, F₇, 41) (dual of [57, 6, 42]-code), using
  - code C₀ for uÂ =Â 3 by de Boer and Brouwer [i]

Mode: Constructive and linear.

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