MinT - Information on Result #2272527

Information on Result #2272527

Linear OA(4¹⁹², 262200, F₄, 27) (dual of [262200, 262008, 28]-code), using 1 times code embedding in larger space based on linear OA(4¹⁹¹, 262199, F₄, 27) (dual of [262199, 262008, 28]-code), using

constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
1. linear OA(4¹⁸¹, 262144, F₄, 27) (dual of [262144, 261963, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
2. linear OA(4¹³⁶, 262144, F₄, 21) (dual of [262144, 262008, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
3. linear OA(4¹⁰, 55, F₄, 5) (dual of [55, 45, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(4¹⁹², 134952, F₄, 2, 27) (dual of [(134952, 2), 269712, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4¹⁹², 134952, F₄, 3, 27) (dual of [(134952, 3), 404664, 28]-NRT-code)	[i]
3	Digital (165, 192, 134952)-net over F₄	[i]
4	Linear OOA(4¹⁹², 131100, F₄, 2, 27) (dual of [(131100, 2), 262008, 28]-NRT-code)	[i]	OOA Folding
5	Linear OOA(4¹⁹², 87400, F₄, 3, 27) (dual of [(87400, 3), 262008, 28]-NRT-code)	[i]	OOA Folding