MinT - Information on Result #1021107

Information on Result #1021107

Linear OOA(3²⁴², 5592519, F₃, 3, 16) (dual of [(5592519, 3), 16777315, 17]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹⁵, 117, F₃, 3, 5) (dual of [(117, 3), 336, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁴, 40, F₃, 3, 2) (dual of [(40, 3), 116, 3]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(3⁴, 40, F₃, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]
  2. linear OOA(3¹¹, 77, F₃, 3, 5) (dual of [(77, 3), 220, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 11, 77)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3⁷⁶, 2796201, F₃, 3, 8) (dual of [(2796201, 3), 8388527, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(3¹⁵¹, 2796201, F₃, 3, 16) (dual of [(2796201, 3), 8388452, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁴², 2796259, F₃, 5, 16) (dual of [(2796259, 5), 13981053, 17]-NRT-code)	[i]		OOA Folding