MinT - Information on Result #1017844

Information on Result #1017844

Linear OOA(64⁶⁷, 2797568, F₆₄, 3, 14) (dual of [(2797568, 3), 8392637, 15]-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(64⁵³, 2796201, F₆₄, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.