MinT - Information on Result #895475

Information on Result #895475

Linear OOA(4⁷², 32788, F₄, 2, 11) (dual of [(32788, 2), 65504, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁷, 16, F₄, 2, 5) (dual of [(16, 2), 25, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 7, 16)-net over F₄, using
  - linear code embedding found in a computer search [i]
linear OOA(4⁶⁵, 32772, F₄, 2, 11) (dual of [(32772, 2), 65479, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4⁶⁵, 65544, F₄, 11) (dual of [65544, 65479, 12]-code), using
  - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
    1. linear OA(4⁶⁵, 65536, F₄, 11) (dual of [65536, 65471, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(4⁵⁷, 65536, F₄, 10) (dual of [65536, 65479, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(4⁰, 8, F₄, 0) (dual of [8, 8, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

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