MinT - Information on Result #900681

Information on Result #900681

Linear OOA(27¹⁰², 8388602, F₂₇, 2, 15) (dual of [(8388602, 2), 16777102, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27³¹, 4194301, F₂₇, 2, 7) (dual of [(4194301, 2), 8388571, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27³¹, 8388602, F₂₇, 7) (dual of [8388602, 8388571, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(27³¹, large, F₂₇, 7) (dual of [large, large−31, 8]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(27⁷¹, 4194301, F₂₇, 2, 15) (dual of [(4194301, 2), 8388531, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁷¹, 8388602, F₂₇, 15) (dual of [8388602, 8388531, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁷¹, large, F₂₇, 15) (dual of [large, large−71, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(27¹⁰⁴, large, F₂₇, 2, 15)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(27¹⁰⁶, large, F₂₇, 2, 15)	[i]
3	Linear OOA(27¹⁰⁸, large, F₂₇, 2, 15)	[i]
4	Linear OOA(27¹¹⁰, large, F₂₇, 2, 15)	[i]
5	Linear OOA(27¹⁰³, 8388602, F₂₇, 2, 15) (dual of [(8388602, 2), 16777101, 16]-NRT-code)	[i]	OOA Duplication
6	Linear OOA(27¹⁰², 2097150, F₂₇, 18, 15) (dual of [(2097150, 18), 37748598, 16]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row