MinT - Information on Result #1014002

Information on Result #1014002

Linear OOA(7⁸¹, 5619, F₇, 3, 17) (dual of [(5619, 3), 16776, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7⁹, 13, F₇, 3, 8) (dual of [(13, 3), 30, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 9, 13)-net over F₇, using
  - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7⁷², 5606, F₇, 3, 17) (dual of [(5606, 3), 16746, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁷², 16818, F₇, 17) (dual of [16818, 16746, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁷², 16819, F₇, 17) (dual of [16819, 16747, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(7⁷¹, 16808, F₇, 17) (dual of [16808, 16737, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808Â | 7¹⁰âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. linear OA(7⁶¹, 16808, F₇, 15) (dual of [16808, 16747, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808Â | 7¹⁰âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      3. 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁸², 5619, F₇, 3, 17) (dual of [(5619, 3), 16775, 18]-NRT-code)	[i]		OOA Duplication