MinT - Information on Result #895565

Information on Result #895565

Linear OOA(4¹⁵², 4194369, F₄, 2, 15) (dual of [(4194369, 2), 8388586, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹⁹, 68, F₄, 2, 7) (dual of [(68, 2), 117, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁵, 41, F₄, 2, 3) (dual of [(41, 2), 77, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
      - a cap found by Tallinii [i]
  2. linear OOA(4¹⁴, 34, F₄, 2, 7) (dual of [(34, 2), 54, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₄, using
      - trace code for nets [i] based on digital (0, 7, 17)-net over F₁₆, using
        net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
        the rational function field F₁₆(x) [i]
        Niederreiter sequence [i]
linear OOA(4¹³³, 4194301, F₄, 2, 15) (dual of [(4194301, 2), 8388469, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹³³, 8388602, F₄, 15) (dual of [8388602, 8388469, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹³³, large, F₄, 15) (dual of [large, large−133, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.