MinT - Information on Result #1130083

Information on Result #1130083

Linear OOA(2³⁷, 130, F₂, 6, 8) (dual of [(130, 6), 743, 9]-NRT-code), using OA 4-folding and stacking based on linear OA(2³⁷, 520, F₂, 8) (dual of [520, 483, 9]-code), using

discarding factors / shortening the dual code based on linear OA(2³⁷, 522, F₂, 8) (dual of [522, 485, 9]-code), using
- 1 times truncation [i] based on linear OA(2³⁸, 523, F₂, 9) (dual of [523, 485, 10]-code), using
  - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
    1. linear OA(2³⁷, 512, F₂, 9) (dual of [512, 475, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(2²⁸, 512, F₂, 7) (dual of [512, 484, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(2¹⁰, 11, F₂, 9) (dual of [11, 1, 10]-code), using
      - strength reduction [i] based on linear OA(2¹⁰, 11, F₂, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
        dual of repetition code with length 11 [i]
    4. linear OA(2¹, 11, F₂, 1) (dual of [11, 10, 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		This result only	Method
1	Linear OOA(2²²¹, 1398230, F₂, 6, 16) (dual of [(1398230, 6), 8389159, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²²², 1398230, F₂, 6, 17) (dual of [(1398230, 6), 8389158, 18]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs