MinT - Information on Result #1466358

Information on Result #1466358

Linear OOA(3¹⁷¹, 4194346, F₃, 2, 16) (dual of [(4194346, 2), 8388521, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁰, 45, F₃, 2, 8) (dual of [(45, 2), 70, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁰, 45, F₃, 8) (dual of [45, 25, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁰, 46, F₃, 8) (dual of [46, 26, 9]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(3³, 11, F₃, 2) (dual of [11, 8, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
      2. linear OA(3⁵, 11, F₃, 4) (dual of [11, 6, 5]-code), using
        Golay code G(3) [i]
      3. linear OA(3¹², 24, F₃, 8) (dual of [24, 12, 9]-code), using
        extended quadratic residue code Q_e(24,3) [i]
linear OOA(3¹⁵¹, 4194301, F₃, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁵¹, 8388602, F₃, 16) (dual of [8388602, 8388451, 17]-code), using
  - discarding factors / shortening the dual code 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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁷¹, 4194346, F₃, 3, 16) (dual of [(4194346, 3), 12582867, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁷¹, 4194346, F₃, 4, 16) (dual of [(4194346, 4), 16777213, 17]-NRT-code)	[i]
3	Linear OOA(3¹⁷¹, 4194346, F₃, 5, 16) (dual of [(4194346, 5), 20971559, 17]-NRT-code)	[i]
4	Digital (155, 171, 4194346)-net over F₃	[i]