MinT - Information on Result #1011834

Information on Result #1011834

Linear OOA(4⁹⁶, 1398121, F₄, 3, 11) (dual of [(1398121, 3), 4194267, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁷, 16, F₄, 3, 5) (dual of [(16, 3), 41, 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(4⁸⁹, 1398105, F₄, 3, 11) (dual of [(1398105, 3), 4194226, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4⁸⁹, 4194315, F₄, 11) (dual of [4194315, 4194226, 12]-code), using
  - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
    1. linear OA(4⁸⁹, 4194304, F₄, 11) (dual of [4194304, 4194215, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(4⁷⁸, 4194304, F₄, 10) (dual of [4194304, 4194226, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    3. linear OA(4⁰, 11, F₄, 0) (dual of [11, 11, 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.

None.

None.