MinT - Information on Result #953171

Information on Result #953171

Linear OOA(3¹⁷⁸, 177162, F₃, 3, 22) (dual of [(177162, 3), 531308, 23]-NRT-code), using OOA 3-folding based on linear OA(3¹⁷⁸, 531486, F₃, 22) (dual of [531486, 531308, 23]-code), using

constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
1. linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
2. linear OA(3¹³³, 531441, F₃, 17) (dual of [531441, 531308, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
3. linear OA(3⁹, 45, F₃, 4) (dual of [45, 36, 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(3¹⁷⁹, 177162, F₃, 3, 22) (dual of [(177162, 3), 531307, 23]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁷⁷, 177161, F₃, 3, 21) (dual of [(177161, 3), 531306, 22]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3¹⁷⁸, 164336, F₃, 4, 22) (dual of [(164336, 4), 657166, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹⁷⁸, 164336, F₃, 5, 22) (dual of [(164336, 5), 821502, 23]-NRT-code)	[i]
5	Digital (156, 178, 164336)-net over F₃	[i]