MinT - Information on Result #1185881

Information on Result #1185881

Linear OOA(4⁶⁸, 2796488, F₄, 9, 7) (dual of [(2796488, 9), 25168324, 8]-NRT-code), using OOA stacking with additional row based on linear OOA(4⁶⁸, 2796489, F₄, 3, 7) (dual of [(2796489, 3), 8389399, 8]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁷, 288, F₄, 3, 3) (dual of [(288, 3), 857, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(4⁷, 288, F₄, 2, 3) (dual of [(288, 2), 569, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁷, 288, F₄, 3) (dual of [288, 281, 4]-code or 288-cap in PG(6,4)), using
      - product of two caps with tangent hyperplane [i]
2. linear OOA(4⁶¹, 2796201, F₄, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(4⁶¹, large, F₄, 7) (dual of [large, large−61, 8]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (61, 68, 2796488)-net over F₄	[i]		Net Defined by OOA