MinT - Information on Result #1011878

Information on Result #1011878

Linear OOA(4¹²², 2796236, F₄, 3, 13) (dual of [(2796236, 3), 8388586, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹³, 35, F₄, 3, 6) (dual of [(35, 3), 92, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁴, 17, F₄, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on 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 OOA(4⁹, 18, F₄, 3, 6) (dual of [(18, 3), 45, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 9, 18)-net over F₄, using
      - linear code embedding found in a computer search [i]
linear OOA(4¹⁰⁹, 2796201, F₄, 3, 13) (dual of [(2796201, 3), 8388494, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Mode: Constructive and linear.

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