MinT - Information on Result #1684262

Information on Result #1684262

Linear OOA(2¹⁸⁸, 1677975, F₂, 7, 15) (dual of [(1677975, 7), 11745637, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁸⁸, 1677975, F₂, 5, 15) (dual of [(1677975, 5), 8389687, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²⁶, 255, F₂, 5, 7) (dual of [(255, 5), 1249, 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(2¹⁶², 1677720, F₂, 5, 15) (dual of [(1677720, 5), 8388438, 16]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 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(2¹⁸⁸, 1677974, F₂, 8, 15) (dual of [(1677974, 8), 13423604, 16]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁸⁸, 1677974, F₂, 21, 15) (dual of [(1677974, 21), 35237266, 16]-NRT-code)	[i]		OOA Stacking with Additional Row