MinT - Information on Result #1197732

Information on Result #1197732

Digital (42, 55, 88583)-net over F₂₇, using net defined by OOA based on linear OOA(27⁵⁵, 88583, F₂₇, 14, 13) (dual of [(88583, 14), 1240107, 14]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(27⁵⁵, 265750, F₂₇, 2, 13) (dual of [(265750, 2), 531445, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(27⁶, 28, F₂₇, 2, 6) (dual of [(28, 2), 50, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;50,27) [i]
  2. linear OOA(27⁴⁹, 265722, F₂₇, 2, 13) (dual of [(265722, 2), 531395, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(27⁴⁹, 531444, F₂₇, 13) (dual of [531444, 531395, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁴⁹, 531445, F₂₇, 13) (dual of [531445, 531396, 14]-code), using
        constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(27⁴⁹, 531441, F₂₇, 13) (dual of [531441, 531392, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(27⁴⁵, 531441, F₂₇, 12) (dual of [531441, 531396, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(27⁰, 4, F₂₇, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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.