MinT - Information on Result #903630

Information on Result #903630

Linear OOA(64⁵³, 4202367, F₆₄, 2, 11) (dual of [(4202367, 2), 8404681, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹², 8066, F₆₄, 2, 5) (dual of [(8066, 2), 16120, 6]-NRT-code), using
- OOA 2-folding [i] 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(64⁴¹, 4194301, F₆₄, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁴¹, 8388602, F₆₄, 11) (dual of [8388602, 8388561, 12]-code), using
  - discarding factors / shortening the dual code 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.

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

None.