MinT - Information on Result #1703214

Information on Result #1703214

Linear OOA(2²¹³, 3307, F₂, 8, 30) (dual of [(3307, 8), 26243, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹³, 3307, F₂, 4, 30) (dual of [(3307, 4), 13015, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹³, 4100, F₂, 4, 30) (dual of [(4100, 4), 16187, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2²¹³, 16400, F₂, 30) (dual of [16400, 16187, 31]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2²¹¹, 16398, F₂, 30) (dual of [16398, 16187, 31]-code), using
    - 1 times truncation [i] based on linear OA(2²¹², 16399, F₂, 31) (dual of [16399, 16187, 32]-code), using
      - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
        linear OA(2²¹¹, 16384, F₂, 31) (dual of [16384, 16173, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(2¹⁹⁷, 16384, F₂, 29) (dual of [16384, 16187, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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(2²¹³, 1653, F₂, 40, 30) (dual of [(1653, 40), 65907, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row