MinT - Information on Result #1014085

Information on Result #1014085

Linear OOA(7¹⁰³, 5619, F₇, 3, 21) (dual of [(5619, 3), 16754, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹¹, 13, F₇, 3, 10) (dual of [(13, 3), 28, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 11, 13)-net over F₇, using
  - 2 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7⁹², 5606, F₇, 3, 21) (dual of [(5606, 3), 16726, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁹², 16818, F₇, 21) (dual of [16818, 16726, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁹², 16819, F₇, 21) (dual of [16819, 16727, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(7⁹¹, 16808, F₇, 21) (dual of [16808, 16717, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808Â | 7¹⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(7⁸¹, 16808, F₇, 19) (dual of [16808, 16727, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808Â | 7¹⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (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(7¹⁰⁴, 5619, F₇, 3, 21) (dual of [(5619, 3), 16753, 22]-NRT-code)	[i]		OOA Duplication