MinT - Information on Result #1190382

Information on Result #1190382

Digital (51, 64, 2809)-net over F₇, using net defined by OOA based on linear OOA(7⁶⁴, 2809, F₇, 15, 13) (dual of [(2809, 15), 42071, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(7⁶⁴, 5619, F₇, 3, 13) (dual of [(5619, 3), 16793, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁷, 13, F₇, 3, 6) (dual of [(13, 3), 32, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 13)-net over F₇, using
      - 6 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
  2. linear OOA(7⁵⁷, 5606, F₇, 3, 13) (dual of [(5606, 3), 16761, 14]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(7⁵⁷, 16818, F₇, 13) (dual of [16818, 16761, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
        linear OA(7⁵⁶, 16807, F₇, 13) (dual of [16807, 16751, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(7⁴⁶, 16807, F₇, 11) (dual of [16807, 16761, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(7¹, 11, F₇, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 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.