MinT - Information on Result #662549

Information on Result #662549

Linear OA(4¹⁰⁹, 262161, F₄, 15) (dual of [262161, 262052, 16]-code), using (u,Â u+v)-construction based on

linear OA(4⁹, 17, F₄, 7) (dual of [17, 8, 8]-code), using
- dual code (with bound on d by constructionÂ Y1) [i] based on
  1. linear OA(4⁸, 17, F₄, 6) (dual of [17, 9, 7]-code), using
    - the BCH-code C(I) with length 17Â | 4⁴âˆ’1, defining interval IÂ =Â {1,4,7,…,16}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  2. nonexistence of linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), because
    - bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
linear OA(4¹⁰⁰, 262144, F₄, 15) (dual of [262144, 262044, 16]-code), using
- an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4¹⁰⁹, 189667, F₄, 2, 15) (dual of [(189667, 2), 379225, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4¹⁰⁹, 189667, F₄, 3, 15) (dual of [(189667, 3), 568892, 16]-NRT-code)	[i]
3	Digital (94, 109, 189667)-net over F₄	[i]