MinT - Information on Result #1682640

Information on Result #1682640

Linear OOA(2¹⁶², 174766, F₂, 7, 17) (dual of [(174766, 7), 1223200, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶², 174766, F₂, 6, 17) (dual of [(174766, 6), 1048434, 18]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁶², 1048596, F₂, 17) (dual of [1048596, 1048434, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁶², 1048597, F₂, 17) (dual of [1048597, 1048435, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
    1. linear OA(2¹⁶¹, 1048576, F₂, 17) (dual of [1048576, 1048415, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(2¹⁴¹, 1048576, F₂, 15) (dual of [1048576, 1048435, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    3. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 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(2¹⁶³, 174766, F₂, 7, 17) (dual of [(174766, 7), 1223199, 18]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁶⁴, 174766, F₂, 7, 17) (dual of [(174766, 7), 1223198, 18]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁵, 174766, F₂, 7, 17) (dual of [(174766, 7), 1223197, 18]-NRT-code)	[i]