MinT - Information on Result #902232

Information on Result #902232

Linear OOA(32¹⁰⁸, 4194814, F₃₂, 2, 19) (dual of [(4194814, 2), 8389520, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁷, 513, F₃₂, 2, 9) (dual of [(513, 2), 1009, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹⁷, 1026, F₃₂, 9) (dual of [1026, 1009, 10]-code), using
  - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
    1. linear OA(32¹⁷, 1024, F₃₂, 9) (dual of [1024, 1007, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(32¹⁵, 1024, F₃₂, 8) (dual of [1024, 1009, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    3. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(32⁹¹, 4194301, F₃₂, 2, 19) (dual of [(4194301, 2), 8388511, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁹¹, 8388602, F₃₂, 19) (dual of [8388602, 8388511, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁹¹, large, F₃₂, 19) (dual of [large, large−91, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’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.