MinT - Information on Result #1542994

Information on Result #1542994

Linear OOA(4²²⁰, 637583, F₄, 3, 27) (dual of [(637583, 3), 1912529, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²²⁰, 637583, F₄, 27) (dual of [637583, 637363, 28]-code), using

discarding factors / shortening the dual code based on linear OA(4²²⁰, 1048602, F₄, 27) (dual of [1048602, 1048382, 28]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(4¹⁹, 25, F₄, 13) (dual of [25, 6, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁹, 26, F₄, 13) (dual of [26, 7, 14]-code), using
      - 2 times truncation [i] based on linear OA(4²¹, 28, F₄, 15) (dual of [28, 7, 16]-code), using
        a quasi-cyclic code by Gulliver and Bhargava [i]
  2. linear OA(4²⁰¹, 1048577, F₄, 27) (dual of [1048577, 1048376, 28]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²²⁰, 127516, F₄, 33, 27) (dual of [(127516, 33), 4207808, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row