MinT - Information on Result #1164506

Information on Result #1164506

Linear OOA(2¹⁵⁷, 4194442, F₂, 8, 11) (dual of [(4194442, 8), 33555379, 12]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹⁵⁷, 4194443, F₂, 5, 11) (dual of [(4194443, 5), 20972058, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹⁷, 142, F₂, 5, 5) (dual of [(142, 5), 693, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹⁷, 142, F₂, 4, 5) (dual of [(142, 4), 551, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 17, 142)-net over F₂, using
      - linear code embedding found in a computer search [i]
2. linear OOA(2¹⁴⁰, 4194301, F₂, 5, 11) (dual of [(4194301, 5), 20971365, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 8388602, F₂, 3, 11) (dual of [(8388602, 3), 25165666, 12]-NRT-code), using
    - discarding factors / shortening the dual code 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 s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.