MinT - Information on Result #1130092

Information on Result #1130092

Linear OOA(2⁴⁹, 1027, F₂, 6, 8) (dual of [(1027, 6), 6113, 9]-NRT-code), using OA 4-folding and stacking based on linear OA(2⁴⁹, 4108, F₂, 8) (dual of [4108, 4059, 9]-code), using

discarding factors / shortening the dual code based on linear OA(2⁴⁹, 4109, F₂, 8) (dual of [4109, 4060, 9]-code), using
- 1 times truncation [i] based on linear OA(2⁵⁰, 4110, F₂, 9) (dual of [4110, 4060, 10]-code), using
  - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
    1. linear OA(2⁴⁹, 4096, F₂, 9) (dual of [4096, 4047, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(2³⁷, 4096, F₂, 7) (dual of [4096, 4059, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(2¹³, 14, F₂, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
      - dual of repetition code with length 14 [i]
    4. linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 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(2⁵¹, 1027, F₂, 6, 8) (dual of [(1027, 6), 6111, 9]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³³, 1399127, F₂, 6, 16) (dual of [(1399127, 6), 8394529, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2²³⁴, 1399127, F₂, 6, 17) (dual of [(1399127, 6), 8394528, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs