MinT - Information on Result #1596376

Information on Result #1596376

Linear OOA(2²¹³, 2919540, F₂, 4, 14) (dual of [(2919540, 4), 11677947, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹³, 2919540, F₂, 2, 14) (dual of [(2919540, 2), 5838867, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹³, 4259837, F₂, 2, 14) (dual of [(4259837, 2), 8519461, 15]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2²¹¹, 4259836, F₂, 2, 14) (dual of [(4259836, 2), 8519461, 15]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁵⁰, 65535, F₂, 2, 7) (dual of [(65535, 2), 131020, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
    2. linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2²¹³, 1459770, F₂, 7, 14) (dual of [(1459770, 7), 10218177, 15]-NRT-code)	[i]		OOA Folding