MinT - Information on Result #1509341

Information on Result #1509341

Linear OOA(2⁵⁴, 3514, F₂, 3, 8) (dual of [(3514, 3), 10488, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁵⁴, 3514, F₂, 2, 8) (dual of [(3514, 2), 6974, 9]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁵⁴, 4103, F₂, 2, 8) (dual of [(4103, 2), 8152, 9]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁵⁴, 4103, F₂, 2, 9) (dual of [(4103, 2), 8152, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2⁵⁴, 8206, F₂, 9) (dual of [8206, 8152, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(6) [i] based on
      1. linear OA(2⁵³, 8192, F₂, 9) (dual of [8192, 8139, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(2⁴⁰, 8192, F₂, 7) (dual of [8192, 8152, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. 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: 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(2²³⁸, 2799715, F₂, 3, 16) (dual of [(2799715, 3), 8398907, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²³⁹, 2799715, F₂, 3, 17) (dual of [(2799715, 3), 8398906, 18]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs