MinT - Information on Result #1702033

Information on Result #1702033

Linear OOA(2¹⁹⁷, 1773, F₂, 8, 31) (dual of [(1773, 8), 13987, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁷, 1773, F₂, 4, 31) (dual of [(1773, 4), 6895, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹⁷, 2051, F₂, 4, 31) (dual of [(2051, 4), 8007, 32]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁹⁷, 8204, F₂, 31) (dual of [8204, 8007, 32]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁹⁷, 8206, F₂, 31) (dual of [8206, 8009, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
      1. linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(2¹⁸³, 8192, F₂, 29) (dual of [8192, 8009, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(2¹⁹⁷, 886, F₂, 40, 31) (dual of [(886, 40), 35243, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row