MinT - Information on Result #1017884

Information on Result #1017884

Linear OOA(64⁷¹, 2797568, F₆₄, 3, 15) (dual of [(2797568, 3), 8392633, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁴, 1367, F₆₄, 3, 7) (dual of [(1367, 3), 4087, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64¹⁴, 4101, F₆₄, 7) (dual of [4101, 4087, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁴, 4102, F₆₄, 7) (dual of [4102, 4088, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(64¹³, 4097, F₆₄, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(64⁹, 4097, F₆₄, 5) (dual of [4097, 4088, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(64¹, 5, F₆₄, 1) (dual of [5, 4, 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]
linear OOA(64⁵⁷, 2796201, F₆₄, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.