MinT - Information on Result #1215160

Information on Result #1215160

Digital (43, 54, 6583)-net over F₈, using (u,Â u+v)-construction based on

digital (2, 7, 28)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁷, 28, F₈, 5, 5) (dual of [(28, 5), 133, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
    - a code by Danev and Olsson [i]
digital (36, 47, 6555)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁴⁷, 6555, F₈, 11, 11) (dual of [(6555, 11), 72058, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(8⁴⁷, 32776, F₈, 11) (dual of [32776, 32729, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁴⁷, 32779, F₈, 11) (dual of [32779, 32732, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(8⁴⁶, 32768, F₈, 11) (dual of [32768, 32722, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(8³⁶, 32768, F₈, 9) (dual of [32768, 32732, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(8¹, 11, F₈, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.