MinT - Information on Result #1665493

Information on Result #1665493

Linear OOA(2¹⁶², 2097278, F₂, 6, 13) (dual of [(2097278, 6), 12583506, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶², 2097278, F₂, 4, 13) (dual of [(2097278, 4), 8388950, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²¹, 127, F₂, 4, 6) (dual of [(127, 4), 487, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
    - linear code embedding found in a computer search [i]
2. linear OOA(2¹⁴¹, 2097151, F₂, 4, 13) (dual of [(2097151, 4), 8388463, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁴¹, 4194302, F₂, 2, 13) (dual of [(4194302, 2), 8388463, 14]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 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(2¹⁶², 2097277, F₂, 7, 13) (dual of [(2097277, 7), 14680777, 14]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁶², 2097277, F₂, 8, 13) (dual of [(2097277, 8), 16778054, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁶², 2097277, F₂, 18, 13) (dual of [(2097277, 18), 37750824, 14]-NRT-code)	[i]