MinT - Information on Result #1014521

Information on Result #1014521

Linear OOA(8¹²⁴, 5592597, F₈, 3, 14) (dual of [(5592597, 3), 16777667, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁸, 195, F₈, 3, 7) (dual of [(195, 3), 567, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁴, 65, F₈, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8⁴, 65, F₈, 2, 3) (dual of [(65, 2), 126, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
        ovoid in PG(3,Â 8) [i]
  2. linear OOA(8¹⁴, 130, F₈, 3, 7) (dual of [(130, 3), 376, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 130)-net over F₈, using
      - trace code for nets [i] based on digital (0, 7, 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]
linear OOA(8¹⁰⁶, 5592402, F₈, 3, 14) (dual of [(5592402, 3), 16777100, 15]-NRT-code), using
- trace code [i] based on linear OOA(64⁵³, 2796201, F₆₄, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.