MinT - Information on Result #901851

Information on Result #901851

Linear OOA(32⁵⁰, 4195293, F₃₂, 2, 9) (dual of [(4195293, 2), 8390536, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32⁹, 992, F₃₂, 2, 4) (dual of [(992, 2), 1975, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁹, 1984, F₃₂, 4) (dual of [1984, 1975, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁹, 1985, F₃₂, 4) (dual of [1985, 1976, 5]-code), using
    - 1 times truncation [i] based on linear OA(32¹⁰, 1986, F₃₂, 5) (dual of [1986, 1976, 6]-code), using
      - (u,Â u+v)-construction [i] based on
        linear OA(32³, 993, F₃₂, 2) (dual of [993, 990, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(32³, 1023, F₃₂, 2) (dual of [1023, 1020, 3]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(32⁷, 993, F₃₂, 5) (dual of [993, 986, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(32⁴¹, 4194301, F₃₂, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁴¹, 8388602, F₃₂, 9) (dual of [8388602, 8388561, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁴¹, large, F₃₂, 9) (dual of [large, large−41, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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.