MinT - Information on Result #1466370

Information on Result #1466370

Linear OOA(3¹⁸⁵, 4194338, F₃, 2, 17) (dual of [(4194338, 2), 8388491, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 37, F₃, 2, 8) (dual of [(37, 2), 55, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁹, 37, F₃, 8) (dual of [37, 18, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁹, 48, F₃, 8) (dual of [48, 29, 9]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(3⁷, 24, F₃, 4) (dual of [24, 17, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁷, 26, F₃, 4) (dual of [26, 19, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 26Â = 3³âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(3¹², 24, F₃, 8) (dual of [24, 12, 9]-code), using
        extended quadratic residue code Q_e(24,3) [i]
linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁸⁵, 4194338, F₃, 3, 17) (dual of [(4194338, 3), 12582829, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁵, 4194338, F₃, 4, 17) (dual of [(4194338, 4), 16777167, 18]-NRT-code)	[i]
3	Linear OOA(3¹⁸⁵, 4194338, F₃, 5, 17) (dual of [(4194338, 5), 20971505, 18]-NRT-code)	[i]
4	Digital (168, 185, 4194338)-net over F₃	[i]