MinT - Information on Result #1193148

Information on Result #1193148

Digital (39, 46, 1594334)-net over F₉, using net defined by OOA based on linear OOA(9⁴⁶, 1594334, F₉, 9, 7) (dual of [(1594334, 9), 14348960, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(9⁴⁶, 1594335, F₉, 3, 7) (dual of [(1594335, 3), 4782959, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9³, 10, F₉, 3, 3) (dual of [(10, 3), 27, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;27,9) [i]
  2. linear OOA(9⁴³, 1594325, F₉, 3, 7) (dual of [(1594325, 3), 4782932, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(9⁴³, 4782975, F₉, 7) (dual of [4782975, 4782932, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁴³, 4782976, F₉, 7) (dual of [4782976, 4782933, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(9⁴³, 4782969, F₉, 7) (dual of [4782969, 4782926, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(9³⁶, 4782969, F₉, 6) (dual of [4782969, 4782933, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.