MinT - Information on Result #1165219

Information on Result #1165219

Linear OOA(2²¹², 1048601, F₂, 8, 16) (dual of [(1048601, 8), 8388596, 17]-NRT-code), using OOA 2-folding based on linear OOA(2²¹², 2097202, F₂, 4, 16) (dual of [(2097202, 4), 8388596, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹², 2097203, F₂, 4, 16) (dual of [(2097203, 4), 8388600, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁸, 53, F₂, 4, 8) (dual of [(53, 4), 184, 9]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁹, 23, F₂, 4, 4) (dual of [(23, 4), 83, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2⁹, 23, F₂, 3, 4) (dual of [(23, 3), 60, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
      2. linear OOA(2¹⁹, 30, F₂, 4, 8) (dual of [(30, 4), 101, 9]-NRT-code), using
        extracting embedded OOA [i] based on digital (11, 19, 30)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁸⁴, 2097150, F₂, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.