MinT - Information on Result #1684820

Information on Result #1684820

Linear OOA(2¹⁹⁶, 2098174, F₂, 7, 15) (dual of [(2098174, 7), 14687022, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁶, 2098174, F₂, 4, 15) (dual of [(2098174, 4), 8392500, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³², 1023, F₂, 4, 7) (dual of [(1023, 4), 4060, 8]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2³², 1023, F₂, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁶⁴, 2097151, F₂, 4, 15) (dual of [(2097151, 4), 8388440, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁶⁴, 4194302, F₂, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(2¹⁹⁶, 2098173, F₂, 8, 15) (dual of [(2098173, 8), 16785188, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁹⁶, 2098173, F₂, 21, 15) (dual of [(2098173, 21), 44061437, 16]-NRT-code)	[i]		OOA Stacking with Additional Row