MinT - Information on Result #1591843

Information on Result #1591843

Linear OOA(2¹⁴⁷, 1192, F₂, 4, 24) (dual of [(1192, 4), 4621, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴⁷, 1192, F₂, 3, 24) (dual of [(1192, 3), 3429, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁴⁷, 1370, F₂, 3, 24) (dual of [(1370, 3), 3963, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹⁴⁷, 4110, F₂, 24) (dual of [4110, 3963, 25]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2¹⁴⁵, 4108, F₂, 24) (dual of [4108, 3963, 25]-code), using
    - 1 times truncation [i] based on linear OA(2¹⁴⁶, 4109, F₂, 25) (dual of [4109, 3963, 26]-code), using
      - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
        linear OA(2¹⁴⁵, 4096, F₂, 25) (dual of [4096, 3951, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(2¹³³, 4096, F₂, 23) (dual of [4096, 3963, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 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(2¹⁴⁷, 596, F₂, 7, 24) (dual of [(596, 7), 4025, 25]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁴⁷, 596, F₂, 8, 24) (dual of [(596, 8), 4621, 25]-NRT-code)	[i]		OOA Folding