MinT - Information on Result #1017711

Information on Result #1017711

Linear OOA(64⁶⁷, 5596564, F₆₄, 3, 11) (dual of [(5596564, 3), 16789625, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁷, 4194301, F₆₄, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(64¹⁷, large, F₆₄, 5) (dual of [large, large−17, 6]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
linear OOA(64⁵⁰, 2798282, F₆₄, 3, 11) (dual of [(2798282, 3), 8394796, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁹, 2081, F₆₄, 3, 5) (dual of [(2081, 3), 6234, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(64², 65, F₆₄, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;193,64) [i]
      2. linear OOA(64⁷, 2016, F₆₄, 3, 5) (dual of [(2016, 3), 6041, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
  2. 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.

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.