MinT - Information on Result #1631682

Information on Result #1631682

Linear OOA(2¹²², 2052, F₂, 5, 19) (dual of [(2052, 5), 10138, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²², 2052, F₂, 4, 19) (dual of [(2052, 4), 8086, 20]-NRT-code), using

2¹ times duplication [i] based on linear OOA(2¹²¹, 2052, F₂, 4, 19) (dual of [(2052, 4), 8087, 20]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹²¹, 8208, F₂, 19) (dual of [8208, 8087, 20]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2¹¹⁹, 8206, F₂, 19) (dual of [8206, 8087, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
      1. linear OA(2¹¹⁸, 8192, F₂, 19) (dual of [8192, 8074, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(2¹⁰⁵, 8192, F₂, 17) (dual of [8192, 8087, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(2¹²³, 2052, F₂, 5, 19) (dual of [(2052, 5), 10137, 20]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹²², 1025, F₂, 25, 19) (dual of [(1025, 25), 25503, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row