MinT - Information on Result #662557

Information on Result #662557

Linear OA(4¹³¹, 4194321, F₄, 15) (dual of [4194321, 4194190, 16]-code), using (u,Â u+v)-construction based on

linear OA(4⁹, 17, F₄, 7) (dual of [17, 8, 8]-code), using
- dual code (with bound on d by constructionÂ Y1) [i] based on
  1. linear OA(4⁸, 17, F₄, 6) (dual of [17, 9, 7]-code), using
    - the BCH-code C(I) with length 17Â | 4⁴âˆ’1, defining interval IÂ =Â {1,4,7,…,16}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  2. nonexistence of linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), because
    - bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
linear OA(4¹²², 4194304, F₄, 15) (dual of [4194304, 4194182, 16]-code), using
- an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

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