MinT - Information on Result #2996544

Information on Result #2996544

Linear OOA(2²²⁴, large, F₂, 8, 11), using 2¹ times duplication based on linear OOA(2²²³, large, F₂, 8, 11), using

4 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁹¹, large, F₂, 8, 11), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁶, 4194305, F₂, 8, 5) (dual of [(4194305, 8), 33554394, 6]-NRT-code), using
    - appending 3 arbitrary columns [i] based on linear OOA(2⁴⁶, 4194305, F₂, 5, 5) (dual of [(4194305, 5), 20971479, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(2⁴⁶, 4194305, F₂, 4, 5) (dual of [(4194305, 4), 16777174, 6]-NRT-code), using
        extracting embedded OOA [i] based on digital (41, 46, 4194305)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2¹⁴⁵, 4194304, F₂, 8, 11) (dual of [(4194304, 8), 33554287, 12]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁵, 3, F₂, 8, 5) (dual of [(3, 8), 19, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(8;19,2) [i]
      2. linear OOA(2¹⁴⁰, 4194301, F₂, 8, 11) (dual of [(4194301, 8), 33554268, 12]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
        OOAs constructed from BCH codes [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.