MinT - Information on Result #902046

Information on Result #902046

Linear OOA(32⁸⁴, 4194814, F₃₂, 2, 15) (dual of [(4194814, 2), 8389544, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹³, 513, F₃₂, 2, 7) (dual of [(513, 2), 1013, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹³, 1026, F₃₂, 7) (dual of [1026, 1013, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(32¹³, 1024, F₃₂, 7) (dual of [1024, 1011, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(32¹¹, 1024, F₃₂, 6) (dual of [1024, 1013, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(32⁷¹, 4194301, F₃₂, 2, 15) (dual of [(4194301, 2), 8388531, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁷¹, 8388602, F₃₂, 15) (dual of [8388602, 8388531, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁷¹, large, F₃₂, 15) (dual of [large, large−71, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.