MinT - Information on Result #2666831

Information on Result #2666831

Linear OOA(2¹⁹², 2796712, F₂, 3, 14) (dual of [(2796712, 3), 8389944, 15]-NRT-code), using 2² times duplication based on linear OOA(2¹⁹⁰, 2796712, F₂, 3, 14) (dual of [(2796712, 3), 8389946, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²⁹, 511, F₂, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁶¹, 2796201, F₂, 3, 14) (dual of [(2796201, 3), 8388442, 15]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁹², 2215340, F₂, 4, 14) (dual of [(2215340, 4), 8861168, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹², 2215340, F₂, 5, 14) (dual of [(2215340, 5), 11076508, 15]-NRT-code)	[i]
3	Linear OOA(2¹⁹², 2215340, F₂, 6, 14) (dual of [(2215340, 6), 13291848, 15]-NRT-code)	[i]
4	Linear OOA(2¹⁹², 2215340, F₂, 7, 14) (dual of [(2215340, 7), 15507188, 15]-NRT-code)	[i]
5	Linear OOA(2¹⁹², 2215340, F₂, 8, 14) (dual of [(2215340, 8), 17722528, 15]-NRT-code)	[i]
6	Digital (178, 192, 2215340)-net over F₂	[i]