MinT - Information on Result #901879

Information on Result #901879

Linear OOA(32⁶⁴, 4718594, F₃₂, 2, 10) (dual of [(4718594, 2), 9437124, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁸, 524293, F₃₂, 2, 5) (dual of [(524293, 2), 1048568, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹⁸, 1048586, F₃₂, 5) (dual of [1048586, 1048568, 6]-code), using
  - constructionÂ X applied to C([0,2]) âŠ‚ C([0,1]) [i] based on
    1. linear OA(32¹⁷, 1048577, F₃₂, 5) (dual of [1048577, 1048560, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
    2. linear OA(32⁹, 1048577, F₃₂, 3) (dual of [1048577, 1048568, 4]-code or 1048577-cap in PG(8,32)), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,1], and minimum distance dÂ â‰¥ |{−1,0,1}|+1Â =Â 4 (BCH-bound) [i]
    3. linear OA(32¹, 9, F₃₂, 1) (dual of [9, 8, 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]
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.