MinT - Information on Result #1079868

Information on Result #1079868

Linear OOA(2¹⁹², 2097661, F₂, 4, 14) (dual of [(2097661, 4), 8390452, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁹, 510, F₂, 4, 7) (dual of [(510, 4), 2011, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2²⁹, 511, F₂, 3, 7) (dual of [(511, 3), 1504, 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: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵⁷, 4194811, F₂, 4, 14) (dual of [(4194811, 4), 16778987, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁶⁰, 4195322, F₂, 4, 14) (dual of [(4195322, 4), 16781028, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs