MinT - Information on Result #945088

Information on Result #945088

Linear OOA(2⁵⁸, 5466, F₂, 3, 9) (dual of [(5466, 3), 16340, 10]-NRT-code), using OOA 3-folding based on linear OA(2⁵⁸, 16398, F₂, 9) (dual of [16398, 16340, 10]-code), using

discarding factors / shortening the dual code based on linear OA(2⁵⁸, 16399, F₂, 9) (dual of [16399, 16341, 10]-code), using
- constructionÂ X applied to C_e(8) âŠ‚ C_e(6) [i] based on
  1. linear OA(2⁵⁷, 16384, F₂, 9) (dual of [16384, 16327, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  2. linear OA(2⁴³, 16384, F₂, 7) (dual of [16384, 16341, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  3. linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2⁵⁸, 5466, F₂, 3, 8) (dual of [(5466, 3), 16340, 9]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2⁵⁸, 5329, F₂, 4, 9) (dual of [(5329, 4), 21258, 10]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2⁵⁸, 5329, F₂, 5, 9) (dual of [(5329, 5), 26587, 10]-NRT-code)	[i]
4	Linear OOA(2⁵⁸, 5329, F₂, 6, 9) (dual of [(5329, 6), 31916, 10]-NRT-code)	[i]
5	Linear OOA(2⁵⁸, 5329, F₂, 7, 9) (dual of [(5329, 7), 37245, 10]-NRT-code)	[i]
6	Linear OOA(2⁵⁸, 5329, F₂, 8, 9) (dual of [(5329, 8), 42574, 10]-NRT-code)	[i]