MinT - Information on Result #1060573

Information on Result #1060573

Linear OOA(3¹⁶¹, 398588, F₃, 4, 19) (dual of [(398588, 4), 1594191, 20]-NRT-code), using OOA 4-folding based on linear OA(3¹⁶¹, 1594352, F₃, 19) (dual of [1594352, 1594191, 20]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁶¹, 1594353, F₃, 19) (dual of [1594353, 1594192, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
  1. linear OA(3¹⁵⁷, 1594323, F₃, 19) (dual of [1594323, 1594166, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. 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]
  3. linear OA(3⁴, 30, F₃, 2) (dual of [30, 26, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
      - Hamming code H(4,3) [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(3¹⁶¹, 398588, F₃, 4, 18) (dual of [(398588, 4), 1594191, 19]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁶², 398588, F₃, 4, 19) (dual of [(398588, 4), 1594190, 20]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹⁶¹, 398588, F₃, 5, 19) (dual of [(398588, 5), 1992779, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Digital (142, 161, 398588)-net over F₃	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound