MinT - Information on Result #1080831

Information on Result #1080831

Linear OOA(3⁶³, large, F₃, 4, 5), using (u,Â u+v)-construction based on

linear OOA(3¹⁵, 7174453, F₃, 4, 2) (dual of [(7174453, 4), 28697797, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(3¹⁵, 7174453, F₃, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(3¹⁵, 7174453, F₃, 2) (dual of [7174453, 7174438, 3]-code), using
    - Hamming code H(15,3) [i]
linear OOA(3⁴⁸, 4194305, F₃, 4, 5) (dual of [(4194305, 4), 16777172, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3², 4, F₃, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(4;14,3) [i]
  2. linear OOA(3⁴⁶, 4194301, F₃, 4, 5) (dual of [(4194301, 4), 16777158, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: Constructive and linear.

Show details for fixed k and m, k and t, m and t.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3⁶³, large, F₃, 4, 4)	[i]		Strength Reduction for OOAs
2	Linear OOA(3⁶³, large, F₃, 4, 3)	[i]		Strength Reduction for OOAs