MinT - Information on Result #1159791

Information on Result #1159791

Linear OOA(2²⁰³, 1206562, F₂, 7, 15) (dual of [(1206562, 7), 8445731, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴¹, 8191, F₂, 7, 7) (dual of [(8191, 7), 57296, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁴¹, 8191, F₂, 6, 7) (dual of [(8191, 6), 49105, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (34, 41, 8191)-net over F₂, using
    - nets constructed from net-embeddable BCH codes [i]
linear OOA(2¹⁶², 1198371, F₂, 7, 15) (dual of [(1198371, 7), 8388435, 16]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2¹⁶², 8388597, F₂, 15) (dual of [8388597, 8388435, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰³, 1206562, F₂, 7, 14) (dual of [(1206562, 7), 8445731, 15]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁴, 1206562, F₂, 7, 15) (dual of [(1206562, 7), 8445730, 16]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁵, 1206562, F₂, 7, 15) (dual of [(1206562, 7), 8445729, 16]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁰³, 1206561, F₂, 8, 15) (dual of [(1206561, 8), 9652285, 16]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(2²⁰³, 1206561, F₂, 21, 15) (dual of [(1206561, 21), 25337578, 16]-NRT-code)	[i]	OOA Stacking with Additional Row