MinT - Information on Result #813186

Information on Result #813186

Linear OOA(3¹³⁷, 797184, F₃, 2, 15) (dual of [(797184, 2), 1594231, 16]-NRT-code), using OOA 2-folding based on linear OA(3¹³⁷, 1594368, F₃, 15) (dual of [1594368, 1594231, 16]-code), using

constructionÂ X applied to C_e(15) âŠ‚ C_e(10) [i] based on
1. linear OA(3¹³¹, 1594323, F₃, 16) (dual of [1594323, 1594192, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
2. linear OA(3⁹², 1594323, F₃, 11) (dual of [1594323, 1594231, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
3. linear OA(3⁶, 45, F₃, 3) (dual of [45, 39, 4]-code or 45-cap in PG(5,3)), using
  - discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
    - large caps in PG(5,Â b) [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(3¹³⁹, 797185, F₃, 2, 15) (dual of [(797185, 2), 1594231, 16]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3¹³⁸, 797184, F₃, 2, 15) (dual of [(797184, 2), 1594230, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹³⁷, 616507, F₃, 3, 15) (dual of [(616507, 3), 1849384, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹³⁷, 616507, F₃, 4, 15) (dual of [(616507, 4), 2465891, 16]-NRT-code)	[i]
5	Linear OOA(3¹³⁷, 616507, F₃, 5, 15) (dual of [(616507, 5), 3082398, 16]-NRT-code)	[i]
6	Digital (122, 137, 616507)-net over F₃	[i]