MinT - Information on Result #1190744

Information on Result #1190744

Digital (68, 86, 1872)-net over F₇, using net defined by OOA based on linear OOA(7⁸⁶, 1872, F₇, 21, 18) (dual of [(1872, 21), 39226, 19]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(7⁸⁶, 5617, F₇, 3, 18) (dual of [(5617, 3), 16765, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7¹⁰, 13, F₇, 3, 9) (dual of [(13, 3), 29, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 10, 13)-net over F₇, using
      - 3 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
  2. linear OOA(7⁷⁶, 5604, F₇, 3, 18) (dual of [(5604, 3), 16736, 19]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(7⁷⁶, 16812, F₇, 18) (dual of [16812, 16736, 19]-code), using
      - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
        linear OA(7⁷⁶, 16807, F₇, 18) (dual of [16807, 16731, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
        linear OA(7⁷¹, 16807, F₇, 17) (dual of [16807, 16736, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(7⁰, 5, F₇, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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.