MinT - Information on Result #1051425

Information on Result #1051425

Linear OOA(2¹⁵⁷, 2097186, F₂, 4, 12) (dual of [(2097186, 4), 8388587, 13]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁵⁷, 4194372, F₂, 2, 12) (dual of [(4194372, 2), 8388587, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁵⁷, 4194373, F₂, 2, 12) (dual of [(4194373, 2), 8388589, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁹, 72, F₂, 2, 6) (dual of [(72, 2), 125, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (13, 19, 72)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.