MinT - Information on Result #2627418

Information on Result #2627418

Linear OOA(3²²², 531463, F₃, 3, 24) (dual of [(531463, 3), 1594167, 25]-NRT-code), using strength reduction based on linear OOA(3²²², 531463, F₃, 3, 25) (dual of [(531463, 3), 1594167, 26]-NRT-code), using

OOA 3-folding [i] based on linear OA(3²²², 1594389, F₃, 25) (dual of [1594389, 1594167, 26]-code), using
- constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
  1. linear OA(3²⁰⁹, 1594324, F₃, 25) (dual of [1594324, 1594115, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  2. linear OA(3¹⁵⁷, 1594324, F₃, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
  3. linear OA(3¹³, 65, F₃, 5) (dual of [65, 52, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹³, 80, F₃, 5) (dual of [80, 67, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(3²²³, 531463, F₃, 3, 24) (dual of [(531463, 3), 1594166, 25]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²²², 531463, F₃, 4, 24) (dual of [(531463, 4), 2125630, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3²²², 531463, F₃, 5, 24) (dual of [(531463, 5), 2657093, 25]-NRT-code)	[i]
4	Digital (198, 222, 531463)-net over F₃	[i]