MinT - Information on Result #1616051

Information on Result #1616051

Linear OOA(2¹⁸⁹, 2097406, F₂, 4, 14) (dual of [(2097406, 4), 8389435, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁶, 255, F₂, 4, 7) (dual of [(255, 4), 994, 8]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
linear OOA(2¹⁶³, 2097151, F₂, 4, 14) (dual of [(2097151, 4), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁶³, 4194302, F₂, 2, 14) (dual of [(4194302, 2), 8388441, 15]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on 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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁸⁹, 2097406, F₂, 5, 14) (dual of [(2097406, 5), 10486841, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁹, 2097406, F₂, 6, 14) (dual of [(2097406, 6), 12584247, 15]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁹, 2097406, F₂, 7, 14) (dual of [(2097406, 7), 14681653, 15]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁹, 2097406, F₂, 8, 14) (dual of [(2097406, 8), 16779059, 15]-NRT-code)	[i]
5	Digital (175, 189, 2097406)-net over F₂	[i]