MinT - Information on Result #2485259

Information on Result #2485259

Linear OOA(3⁸⁸, 2391501, F₃, 2, 9) (dual of [(2391501, 2), 4782914, 10]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3⁸⁶, 2391500, F₃, 2, 9) (dual of [(2391500, 2), 4782914, 10]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁸⁶, 4783000, F₃, 9) (dual of [4783000, 4782914, 10]-code), using
- constructionÂ X4 applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
  1. linear OA(3⁸⁵, 4782970, F₃, 9) (dual of [4782970, 4782885, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OA(3⁵⁷, 4782970, F₃, 7) (dual of [4782970, 4782913, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  3. linear OA(3²⁹, 30, F₃, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
    - dual of repetition code with length 30 [i]
  4. linear OA(3¹, 30, F₃, 1) (dual of [30, 29, 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(3⁸⁹, 2391501, F₃, 2, 9) (dual of [(2391501, 2), 4782913, 10]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹¹⁷, 4783002, F₃, 2, 9) (dual of [(4783002, 2), 9565887, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(3⁸⁸, 2391501, F₃, 3, 9) (dual of [(2391501, 3), 7174415, 10]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3⁸⁸, 2391501, F₃, 4, 9) (dual of [(2391501, 4), 9565916, 10]-NRT-code)	[i]
5	Linear OOA(3⁸⁸, 2391501, F₃, 5, 9) (dual of [(2391501, 5), 11957417, 10]-NRT-code)	[i]
6	Digital (79, 88, 2391501)-net over F₃	[i]