MinT - Information on Result #1703454

Information on Result #1703454

Linear OOA(2²¹⁶, 2097278, F₂, 8, 16) (dual of [(2097278, 8), 16778008, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁶, 2097278, F₂, 4, 16) (dual of [(2097278, 4), 8388896, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³², 128, F₂, 4, 8) (dual of [(128, 4), 480, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³², 128, F₂, 2, 8) (dual of [(128, 2), 224, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2³², 256, F₂, 8) (dual of [256, 224, 9]-code), using
      - 1 times truncation [i] based on linear OA(2³³, 257, F₂, 9) (dual of [257, 224, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 257Â | 2¹⁶âˆ’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, 2097150, F₂, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁸⁴, 8388600, F₂, 16) (dual of [8388600, 8388416, 17]-code), using
    - discarding factors / shortening the dual code 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(2²¹⁶, 2097277, F₂, 24, 16) (dual of [(2097277, 24), 50334432, 17]-NRT-code)	[i]		OOA Stacking with Additional Row