MinT - Information on Result #680228

Information on Result #680228

Linear OA(4²⁵⁴, 1059, F₄, 65) (dual of [1059, 805, 66]-code), using constructionÂ X applied to C([0,32]) âŠ‚ C([0,28]) based on

linear OA(4²⁴¹, 1025, F₄, 65) (dual of [1025, 784, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025Â | 4¹⁰âˆ’1, defining interval IÂ =Â [0,32], and minimum distance dÂ â‰¥ |{−32,−31,…,32}|+1Â =Â 66 (BCH-bound) [i]
linear OA(4²¹¹, 1025, F₄, 57) (dual of [1025, 814, 58]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025Â | 4¹⁰âˆ’1, defining interval IÂ =Â [0,28], and minimum distance dÂ â‰¥ |{−28,−27,…,28}|+1Â =Â 58 (BCH-bound) [i]
linear OA(4¹³, 34, F₄, 7) (dual of [34, 21, 8]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
    - ovoid in PG(3,Â 4) [i]
  2. 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]

Mode: Constructive and linear.

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