MinT - Information on Result #1017665

Information on Result #1017665

Linear OOA(64⁴⁹, 2804266, F₆₄, 3, 10) (dual of [(2804266, 3), 8412749, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹², 8065, F₆₄, 3, 5) (dual of [(8065, 3), 24183, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(64¹², 16131, F₆₄, 5) (dual of [16131, 16119, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(64¹², 16132, F₆₄, 5) (dual of [16132, 16120, 6]-code), using
    - generalized (u,Â u+v)-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(64¹, 4033, F₆₄, 1) (dual of [4033, 4032, 2]-code) (see above)
      3. 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]
      4. linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁶⁶, 5608532, F₆₄, 3, 10) (dual of [(5608532, 3), 16825530, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs