MinT - Information on Result #2272600

Information on Result #2272600

Linear OA(4²⁰¹, 262200, F₄, 28) (dual of [262200, 261999, 29]-code), using 1 times code embedding in larger space based on linear OA(4²⁰⁰, 262199, F₄, 28) (dual of [262199, 261999, 29]-code), using

constructionÂ X applied to C_e(28) âŠ‚ C_e(21) [i] based on
1. linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
2. linear OA(4¹⁴⁵, 262144, F₄, 22) (dual of [262144, 261999, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(4²⁰¹, 150433, F₄, 2, 28) (dual of [(150433, 2), 300665, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4²⁰¹, 150433, F₄, 3, 28) (dual of [(150433, 3), 451098, 29]-NRT-code)	[i]
3	Digital (173, 201, 150433)-net over F₄	[i]
4	Linear OOA(4²⁰¹, 131100, F₄, 2, 28) (dual of [(131100, 2), 261999, 29]-NRT-code)	[i]	OOA Folding
5	Linear OOA(4²⁰¹, 87400, F₄, 3, 28) (dual of [(87400, 3), 261999, 29]-NRT-code)	[i]	OOA Folding