MinT - Information on Result #1081203

Information on Result #1081203

Linear OOA(3²¹³, 4194302, F₃, 4, 15) (dual of [(4194302, 4), 16776995, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶¹, 2796200, F₃, 4, 7) (dual of [(2796200, 4), 11184739, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3⁶¹, 8388601, F₃, 7) (dual of [8388601, 8388540, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(3¹⁵², 2097151, F₃, 4, 15) (dual of [(2097151, 4), 8388452, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁵², 4194302, F₃, 2, 15) (dual of [(4194302, 2), 8388452, 16]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁵⁰, 4194301, F₃, 2, 15) (dual of [(4194301, 2), 8388452, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁵⁰, 8388602, F₃, 15) (dual of [8388602, 8388452, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], 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		This result only	Method
1	Linear OOA(3²¹⁴, 4194302, F₃, 4, 15) (dual of [(4194302, 4), 16776994, 16]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²¹⁵, 4194302, F₃, 4, 15) (dual of [(4194302, 4), 16776993, 16]-NRT-code)	[i]		OOA Duplication