MinT - Information on Result #1165478

Information on Result #1165478

Linear OOA(2²²⁸, 1048589, F₂, 8, 18) (dual of [(1048589, 8), 8388484, 19]-NRT-code), using OOA 2-folding based on linear OOA(2²²⁸, 2097178, F₂, 4, 18) (dual of [(2097178, 4), 8388484, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²⁸, 2097179, F₂, 4, 18) (dual of [(2097179, 4), 8388488, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 29, F₂, 4, 9) (dual of [(29, 4), 95, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 21, 29)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2²⁰⁷, 2097150, F₂, 4, 18) (dual of [(2097150, 4), 8388393, 19]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2²⁰⁷, 8388600, F₂, 18) (dual of [8388600, 8388393, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.