MinT - Information on Result #901902

Information on Result #901902

Linear OOA(32⁶⁵, 4210689, F₃₂, 2, 11) (dual of [(4210689, 2), 8421313, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁴, 16388, F₃₂, 2, 5) (dual of [(16388, 2), 32762, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹⁴, 32776, F₃₂, 5) (dual of [32776, 32762, 6]-code), using
  - constructionÂ X applied to C([0,2]) âŠ‚ C([0,1]) [i] based on
    1. linear OA(32¹³, 32769, F₃₂, 5) (dual of [32769, 32756, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’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(32⁷, 32769, F₃₂, 3) (dual of [32769, 32762, 4]-code or 32769-cap in PG(6,32)), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’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, 7, F₃₂, 1) (dual of [7, 6, 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(32⁵¹, 4194301, F₃₂, 2, 11) (dual of [(4194301, 2), 8388551, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁵¹, 8388602, F₃₂, 11) (dual of [8388602, 8388551, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁵¹, large, F₃₂, 11) (dual of [large, large−51, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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.