MinT - Information on Result #2496142

Information on Result #2496142

Linear OOA(4²⁴⁴, 4194542, F₄, 2, 23) (dual of [(4194542, 2), 8388840, 24]-NRT-code), using 4¹ times duplication based on linear OOA(4²⁴³, 4194542, F₄, 2, 23) (dual of [(4194542, 2), 8388841, 24]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(4²⁴¹, 4194541, F₄, 2, 23) (dual of [(4194541, 2), 8388841, 24]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4³⁶, 240, F₄, 2, 11) (dual of [(240, 2), 444, 12]-NRT-code), using
    - extracting embedded OOA [i] based on digital (25, 36, 240)-net over F₄, using
      - trace code for nets [i] based on digital (1, 12, 80)-net over F₆₄, using
        net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
  2. 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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.