MinT - Information on Result #2487113

Information on Result #2487113

Linear OOA(3¹⁸⁵, 29537, F₃, 2, 27) (dual of [(29537, 2), 58889, 28]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3¹⁸³, 29536, F₃, 2, 27) (dual of [(29536, 2), 58889, 28]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁸³, 59072, F₃, 27) (dual of [59072, 58889, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹⁸², 59071, F₃, 27) (dual of [59071, 58889, 28]-code), using
  - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(3¹⁸¹, 59050, F₃, 27) (dual of [59050, 58869, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    2. linear OA(3¹⁶¹, 59050, F₃, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. linear OA(3¹, 21, F₃, 1) (dual of [21, 20, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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, 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(3¹⁸⁵, 21277, F₃, 3, 27) (dual of [(21277, 3), 63646, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁵, 21277, F₃, 4, 27) (dual of [(21277, 4), 84923, 28]-NRT-code)	[i]
3	Linear OOA(3¹⁸⁵, 21277, F₃, 5, 27) (dual of [(21277, 5), 106200, 28]-NRT-code)	[i]
4	Digital (158, 185, 21277)-net over F₃	[i]