MinT - Information on Result #824187

Information on Result #824187

Linear OOA(4¹⁷⁶, 131101, F₄, 2, 25) (dual of [(131101, 2), 262026, 26]-NRT-code), using OOA 2-folding based on linear OA(4¹⁷⁶, 262202, F₄, 25) (dual of [262202, 262026, 26]-code), using

constructionÂ X applied to C_e(24) âŠ‚ C_e(17) [i] based on
1. linear OA(4¹⁶³, 262144, F₄, 25) (dual of [262144, 261981, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
2. linear OA(4¹¹⁸, 262144, F₄, 18) (dual of [262144, 262026, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
3. linear OA(4¹³, 58, F₄, 6) (dual of [58, 45, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹³, 63, F₄, 6) (dual of [63, 50, 7]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(4¹⁷⁸, 131102, F₄, 2, 25) (dual of [(131102, 2), 262026, 26]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁷⁷, 131101, F₄, 2, 25) (dual of [(131101, 2), 262025, 26]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(4¹⁷⁵, 131100, F₄, 2, 24) (dual of [(131100, 2), 262025, 25]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(4¹⁷⁶, 131101, F₄, 3, 25) (dual of [(131101, 3), 393127, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Digital (151, 176, 131101)-net over F₄	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound