MinT - Information on Result #1190318

Information on Result #1190318

Digital (77, 89, 960809)-net over F₇, using net defined by OOA based on linear OOA(7⁸⁹, 960809, F₇, 15, 12) (dual of [(960809, 15), 14412046, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(7⁸⁹, 1921619, F₇, 3, 12) (dual of [(1921619, 3), 5764768, 13]-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(7⁸², 1921606, F₇, 3, 12) (dual of [(1921606, 3), 5764736, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(7⁸², 5764818, F₇, 12) (dual of [5764818, 5764736, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(9) [i] based on
        linear OA(7⁸¹, 5764801, F₇, 12) (dual of [5764801, 5764720, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(7⁶⁵, 5764801, F₇, 10) (dual of [5764801, 5764736, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 7⁸âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(7¹, 17, F₇, 1) (dual of [17, 16, 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.