MinT - Information on Result #662310

Information on Result #662310

Linear OA(4²¹⁵, 65563, F₄, 33) (dual of [65563, 65348, 34]-code), using (u,Â u+v)-construction based on

linear OA(4²², 26, F₄, 16) (dual of [26, 4, 17]-code), using
- juxtaposition [i] based on
  1. linear OA(4⁵, 9, F₄, 4) (dual of [9, 4, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁵, 11, F₄, 4) (dual of [11, 6, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]
  2. linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
    - projective code from ovoid in PG(3,Â 4) [i]
linear OA(4¹⁹³, 65537, F₄, 33) (dual of [65537, 65344, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4²¹⁵, 59277, F₄, 2, 33) (dual of [(59277, 2), 118339, 34]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(4²¹⁵, 59277, F₄, 3, 33) (dual of [(59277, 3), 177616, 34]-NRT-code)	[i]
3	Digital (182, 215, 59277)-net over F₄	[i]