MinT - Information on Result #952555

Information on Result #952555

Linear OOA(3¹¹⁶, 59058, F₃, 3, 16) (dual of [(59058, 3), 177058, 17]-NRT-code), using OOA 3-folding based on linear OA(3¹¹⁶, 177174, F₃, 16) (dual of [177174, 177058, 17]-code), using

1 times code embedding in larger space [i] based on linear OA(3¹¹⁵, 177173, F₃, 16) (dual of [177173, 177058, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
  1. linear OA(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(3⁸⁹, 177147, F₃, 13) (dual of [177147, 177058, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(3⁴, 26, F₃, 2) (dual of [26, 22, 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(3¹¹⁶, 59058, F₃, 3, 15) (dual of [(59058, 3), 177058, 16]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹¹⁷, 59058, F₃, 3, 16) (dual of [(59058, 3), 177057, 17]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹¹⁸, 59058, F₃, 3, 16) (dual of [(59058, 3), 177056, 17]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹¹⁶, 59058, F₃, 4, 16) (dual of [(59058, 4), 236116, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(3¹¹⁶, 59058, F₃, 5, 16) (dual of [(59058, 5), 295174, 17]-NRT-code)	[i]
6	Digital (100, 116, 59058)-net over F₃	[i]