MinT - Information on Result #1631218

Information on Result #1631218

Linear OOA(2¹¹⁰, 1188, F₂, 5, 18) (dual of [(1188, 5), 5830, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁰, 1188, F₂, 3, 18) (dual of [(1188, 3), 3454, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹¹⁰, 1369, F₂, 3, 18) (dual of [(1369, 3), 3997, 19]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹¹⁰, 1369, F₂, 3, 19) (dual of [(1369, 3), 3997, 20]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹¹⁰, 4107, F₂, 19) (dual of [4107, 3997, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹¹⁰, 4109, F₂, 19) (dual of [4109, 3999, 20]-code), using
      - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
        linear OA(2¹⁰⁹, 4096, F₂, 19) (dual of [4096, 3987, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(2⁹⁷, 4096, F₂, 17) (dual of [4096, 3999, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(2¹¹⁰, 593, F₂, 25, 18) (dual of [(593, 25), 14715, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row