MinT - Information on Result #1832996

Information on Result #1832996

OOA(32⁶⁶, 4325377, S₃₂, 2, 11), using discarding parts of the base based on linear OOA(64⁵⁵, 4325377, F₆₄, 2, 11) (dual of [(4325377, 2), 8650699, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(64¹⁴, 131076, F₆₄, 2, 5) (dual of [(131076, 2), 262138, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64¹⁴, 262152, F₆₄, 5) (dual of [262152, 262138, 6]-code), using
    - constructionÂ X applied to C([0,2]) âŠ‚ C([0,1]) [i] based on
      1. linear OA(64¹³, 262145, F₆₄, 5) (dual of [262145, 262132, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’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(64⁷, 262145, F₆₄, 3) (dual of [262145, 262138, 4]-code or 262145-cap in PG(6,64)), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,1], and minimum distance dÂ â‰¥ |{−1,0,1}|+1Â =Â 4 (BCH-bound) [i]
      3. linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OOA(64⁴¹, 4194301, F₆₄, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64⁴¹, 8388602, F₆₄, 11) (dual of [8388602, 8388561, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive.

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.