MinT - Information on Result #1014298

Information on Result #1014298

Linear OOA(8⁹⁰, 5592662, F₈, 3, 9) (dual of [(5592662, 3), 16777896, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²⁵, 4194301, F₈, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8²⁵, 8388602, F₈, 4) (dual of [8388602, 8388577, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(8²⁵, large, F₈, 4) (dual of [large, large−25, 5]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
linear OOA(8⁶⁵, 2796331, F₈, 3, 9) (dual of [(2796331, 3), 8388928, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁸, 130, F₈, 3, 4) (dual of [(130, 3), 382, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 8, 130)-net over F₈, using
      - trace code for nets [i] based on digital (0, 4, 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(8⁵⁷, 2796201, F₈, 3, 9) (dual of [(2796201, 3), 8388546, 10]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8⁵⁷, large, F₈, 9) (dual of [large, large−57, 10]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.