MinT - Information on Result #894256

Information on Result #894256

Linear OOA(2²²⁰, 4718588, F₂, 2, 14) (dual of [(4718588, 2), 9436956, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵⁹, 524287, F₂, 2, 7) (dual of [(524287, 2), 1048515, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (52, 59, 524287)-net over F₂, using
  - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
  - discarding factors / shortening the dual code 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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²²², 4718589, F₂, 2, 14) (dual of [(4718589, 2), 9436956, 15]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²²⁰, 4538161, F₂, 3, 14) (dual of [(4538161, 3), 13614263, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²²⁰, 4538161, F₂, 4, 14) (dual of [(4538161, 4), 18152424, 15]-NRT-code)	[i]
4	Linear OOA(2²²⁰, 4538161, F₂, 5, 14) (dual of [(4538161, 5), 22690585, 15]-NRT-code)	[i]
5	Linear OOA(2²²⁰, 4538161, F₂, 6, 14) (dual of [(4538161, 6), 27228746, 15]-NRT-code)	[i]
6	Linear OOA(2²²⁰, 4538161, F₂, 7, 14) (dual of [(4538161, 7), 31766907, 15]-NRT-code)	[i]
7	Linear OOA(2²²⁰, 4538161, F₂, 8, 14) (dual of [(4538161, 8), 36305068, 15]-NRT-code)	[i]
8	Digital (206, 220, 4538161)-net over F₂	[i]
9	Linear OOA(2²²⁰, 2359294, F₂, 4, 14) (dual of [(2359294, 4), 9436956, 15]-NRT-code)	[i]	OOA Folding