MinT - Information on Result #901872

Information on Result #901872

Linear OOA(32⁵⁷, 4195790, F₃₂, 2, 10) (dual of [(4195790, 2), 8391523, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹¹, 1489, F₃₂, 2, 5) (dual of [(1489, 2), 2967, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹¹, 2978, F₃₂, 5) (dual of [2978, 2967, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(32¹¹, 2979, F₃₂, 5) (dual of [2979, 2968, 6]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(32¹, 993, F₃₂, 1) (dual of [993, 992, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. 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]
      3. linear OA(32⁷, 993, F₃₂, 5) (dual of [993, 986, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(32⁴⁶, 4194301, F₃₂, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁴⁶, 8388602, F₃₂, 10) (dual of [8388602, 8388556, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁴⁶, large, F₃₂, 10) (dual of [large, large−46, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.