MinT - Information on Result #1599293

Information on Result #1599293

Linear OOA(2²⁴⁴, 2807123, F₂, 4, 16) (dual of [(2807123, 4), 11228248, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁴, 2807123, F₂, 3, 16) (dual of [(2807123, 3), 8421125, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁰, 10922, F₂, 3, 8) (dual of [(10922, 3), 32706, 9]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁶⁰, 32766, F₂, 8) (dual of [32766, 32706, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁶⁰, 32768, F₂, 8) (dual of [32768, 32708, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁶¹, 32769, F₂, 9) (dual of [32769, 32708, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’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(2²⁴⁴, 1403561, F₂, 7, 16) (dual of [(1403561, 7), 9824683, 17]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴⁴, 1403561, F₂, 8, 16) (dual of [(1403561, 8), 11228244, 17]-NRT-code)	[i]		OOA Folding