MinT - Information on Result #2467774

Information on Result #2467774

Linear OOA(3¹⁴⁹, 2391509, F₃, 2, 15) (dual of [(2391509, 2), 4782869, 16]-NRT-code), using 1 step truncation based on linear OOA(3¹⁵⁰, 2391510, F₃, 2, 16) (dual of [(2391510, 2), 4782870, 17]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁵⁰, 4783020, F₃, 16) (dual of [4783020, 4782870, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(10) [i] based on
  1. linear OA(3¹⁴¹, 4782969, F₃, 16) (dual of [4782969, 4782828, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(3⁹⁹, 4782969, F₃, 11) (dual of [4782969, 4782870, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(3⁹, 51, F₃, 4) (dual of [51, 42, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3¹⁴⁹, 1849542, F₃, 3, 15) (dual of [(1849542, 3), 5548477, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁴⁹, 1849542, F₃, 4, 15) (dual of [(1849542, 4), 7398019, 16]-NRT-code)	[i]
3	Linear OOA(3¹⁴⁹, 1849542, F₃, 5, 15) (dual of [(1849542, 5), 9247561, 16]-NRT-code)	[i]
4	Digital (134, 149, 1849542)-net over F₃	[i]