MinT - Information on Result #895738

Information on Result #895738

Linear OOA(4²²⁶, 4194329, F₄, 2, 23) (dual of [(4194329, 2), 8388432, 24]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²¹, 28, F₄, 2, 11) (dual of [(28, 2), 35, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(4¹⁴, 14, F₄, 2, 11) (dual of [(14, 2), 14, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,16P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
linear OOA(4²⁰⁵, 4194301, F₄, 2, 23) (dual of [(4194301, 2), 8388397, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²⁰⁵, 8388602, F₄, 23) (dual of [8388602, 8388397, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁰⁵, large, F₄, 23) (dual of [large, large−205, 24]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Mode: Constructive and linear.

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