MinT - Information on Result #1017700

Information on Result #1017700

Linear OOA(64⁵², 2802250, F₆₄, 3, 11) (dual of [(2802250, 3), 8406698, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹¹, 6049, F₆₄, 3, 5) (dual of [(6049, 3), 18136, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(64¹¹, 12099, F₆₄, 5) (dual of [12099, 12088, 6]-code), using
  - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
    1. linear OA(64¹, 4033, F₆₄, 1) (dual of [4033, 4032, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OA(64³, 4033, F₆₄, 2) (dual of [4033, 4030, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
        Hamming code H(3,64) [i]
    3. linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
      - a code by Danev and Olsson [i]
linear OOA(64⁴¹, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁶⁹, 5604500, F₆₄, 3, 11) (dual of [(5604500, 3), 16813431, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs