MinT - Information on Result #1684332

Information on Result #1684332

Linear OOA(2¹⁸⁹, 2097406, F₂, 7, 14) (dual of [(2097406, 7), 14681653, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁸⁹, 2097406, F₂, 4, 14) (dual of [(2097406, 4), 8389435, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²⁶, 255, F₂, 4, 7) (dual of [(255, 4), 994, 8]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁶³, 2097151, F₂, 4, 14) (dual of [(2097151, 4), 8388441, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹⁶³, 4194302, F₂, 2, 14) (dual of [(4194302, 2), 8388441, 15]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on 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(2¹⁸⁹, 2097405, F₂, 8, 14) (dual of [(2097405, 8), 16779051, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁸⁹, 2097405, F₂, 21, 14) (dual of [(2097405, 21), 44045316, 15]-NRT-code)	[i]		OOA Stacking with Additional Row