MinT - Information on Result #1221921

Information on Result #1221921

Digital (30, 39, 133212)-net over F₂₇, using (u,Â u+v)-construction based on

digital (2, 6, 351)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁶, 351, F₂₇, 4, 4) (dual of [(351, 4), 1398, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(27⁶, 702, F₂₇, 4) (dual of [702, 696, 5]-code), using
    - 1 times truncation [i] based on linear OA(27⁷, 703, F₂₇, 5) (dual of [703, 696, 6]-code), using
      - a code by Danev and Olsson [i]
digital (24, 33, 132861)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27³³, 132861, F₂₇, 9, 9) (dual of [(132861, 9), 1195716, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(27³³, 531445, F₂₇, 9) (dual of [531445, 531412, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(27³³, 531441, F₂₇, 9) (dual of [531441, 531408, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(27²⁹, 531441, F₂₇, 8) (dual of [531441, 531412, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. 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.