MinT - Information on Result #1430122

Information on Result #1430122

Linear OOA(4²¹⁴, 56683, F₄, 2, 33) (dual of [(56683, 2), 113152, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²¹⁴, 56683, F₄, 33) (dual of [56683, 56469, 34]-code), using

discarding factors / shortening the dual code based on linear OA(4²¹⁴, 65561, F₄, 33) (dual of [65561, 65347, 34]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(4²¹, 24, F₄, 16) (dual of [24, 3, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²¹, 25, F₄, 16) (dual of [25, 4, 17]-code), using
      - 3 times truncation [i] based on linear OA(4²⁴, 28, F₄, 19) (dual of [28, 4, 20]-code), using
        an explicit generator matrix [i]
  2. linear OA(4¹⁹³, 65537, F₄, 33) (dual of [65537, 65344, 34]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (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(4²¹⁴, 28341, F₄, 3, 33) (dual of [(28341, 3), 84809, 34]-NRT-code)	[i]		OOA Folding