MinT - Information on Result #1667383

Information on Result #1667383

Linear OOA(2¹⁹³, 2927273, F₂, 6, 13) (dual of [(2927273, 6), 17563445, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹³, 2927273, F₂, 3, 13) (dual of [(2927273, 3), 8781626, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵⁴, 131072, F₂, 3, 6) (dual of [(131072, 3), 393162, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁵⁴, 131072, F₂, 2, 6) (dual of [(131072, 2), 262090, 7]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2⁵², 131071, F₂, 2, 6) (dual of [(131071, 2), 262090, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
        1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
2. linear OOA(2¹³⁹, 2796201, F₂, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
  - OOA 3-folding [i] 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(2¹⁹³, 2927272, F₂, 7, 13) (dual of [(2927272, 7), 20490711, 14]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁹³, 2927272, F₂, 8, 13) (dual of [(2927272, 8), 23417983, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁹³, 2927272, F₂, 18, 13) (dual of [(2927272, 18), 52690703, 14]-NRT-code)	[i]