MinT - Information on Result #1060581

Information on Result #1060581

Linear OOA(3¹⁷³, 1195750, F₃, 4, 19) (dual of [(1195750, 4), 4782827, 20]-NRT-code), using OOA 4-folding based on linear OA(3¹⁷³, 4783000, F₃, 19) (dual of [4783000, 4782827, 20]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁷³, 4783001, F₃, 19) (dual of [4783001, 4782828, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
  1. linear OA(3¹⁶⁹, 4782969, F₃, 19) (dual of [4782969, 4782800, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. 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]
  3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 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(3¹⁷³, 1195750, F₃, 4, 18) (dual of [(1195750, 4), 4782827, 19]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁷⁴, 1195750, F₃, 4, 19) (dual of [(1195750, 4), 4782826, 20]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹⁷³, 1195750, F₃, 5, 19) (dual of [(1195750, 5), 5978577, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Digital (154, 173, 1195750)-net over F₃	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound