MinT - Information on Result #1597725

Information on Result #1597725

Linear OOA(2²²⁸, 2331689, F₂, 4, 16) (dual of [(2331689, 4), 9326528, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²⁸, 2331689, F₂, 3, 16) (dual of [(2331689, 3), 6994839, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²⁸, 2796883, F₂, 3, 16) (dual of [(2796883, 3), 8390421, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁴, 682, F₂, 3, 8) (dual of [(682, 3), 2002, 9]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2⁴⁴, 2046, F₂, 8) (dual of [2046, 2002, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁴⁴, 2048, F₂, 8) (dual of [2048, 2004, 9]-code), using
        1 times truncation [i] based on linear OA(2⁴⁵, 2049, F₂, 9) (dual of [2049, 2004, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OOA(2¹⁸⁴, 2796201, F₂, 3, 16) (dual of [(2796201, 3), 8388419, 17]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁸, 1165844, F₂, 8, 16) (dual of [(1165844, 8), 9326524, 17]-NRT-code)	[i]		OOA Folding