MinT - Information on Result #2494772

Information on Result #2494772

Linear OOA(4¹²⁹, 4194497, F₄, 2, 13) (dual of [(4194497, 2), 8388865, 14]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹²⁷, 4194496, F₄, 2, 13) (dual of [(4194496, 2), 8388865, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4¹⁸, 195, F₄, 2, 6) (dual of [(195, 2), 372, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (12, 18, 195)-net over F₄, using
    - trace code for nets [i] based on digital (0, 6, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
2. linear OOA(4¹⁰⁹, 4194301, F₄, 2, 13) (dual of [(4194301, 2), 8388493, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁰⁹, 8388602, F₄, 13) (dual of [8388602, 8388493, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.