MinT - Information on Result #1665894

Information on Result #1665894

Linear OOA(2¹⁶⁹, 2097662, F₂, 6, 13) (dual of [(2097662, 6), 12585803, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶⁹, 2097662, F₂, 4, 13) (dual of [(2097662, 4), 8390479, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³⁰, 512, F₂, 4, 6) (dual of [(512, 4), 2018, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³⁰, 512, F₂, 2, 6) (dual of [(512, 2), 994, 7]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2²⁸, 511, F₂, 2, 6) (dual of [(511, 2), 994, 7]-NRT-code), using
      - OOAs constructed from BCH codes [i]
2. linear OOA(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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(2¹⁶⁹, 2097661, F₂, 7, 13) (dual of [(2097661, 7), 14683458, 14]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁶⁹, 2097661, F₂, 8, 13) (dual of [(2097661, 8), 16781119, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁹, 2097661, F₂, 18, 13) (dual of [(2097661, 18), 37757729, 14]-NRT-code)	[i]