MinT - Information on Result #900849

Information on Result #900849

Linear OOA(27¹⁰⁹, 4194668, F₂₇, 2, 19) (dual of [(4194668, 2), 8389227, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27¹⁸, 367, F₂₇, 2, 9) (dual of [(367, 2), 716, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27¹⁸, 734, F₂₇, 9) (dual of [734, 716, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(27¹⁸, 735, F₂₇, 9) (dual of [735, 717, 10]-code), using
    - constructionÂ X applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
      1. linear OA(27¹⁷, 730, F₂₇, 9) (dual of [730, 713, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 730Â | 27⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
      2. linear OA(27¹³, 730, F₂₇, 7) (dual of [730, 717, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 730Â | 27⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      3. linear OA(27¹, 5, F₂₇, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(27⁹¹, 4194301, F₂₇, 2, 19) (dual of [(4194301, 2), 8388511, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁹¹, 8388602, F₂₇, 19) (dual of [8388602, 8388511, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁹¹, large, F₂₇, 19) (dual of [large, large−91, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [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.