MinT - Information on Result #1698144

Information on Result #1698144

Linear OOA(2¹³⁰, 12921, F₂, 8, 17) (dual of [(12921, 8), 103238, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³⁰, 12921, F₂, 5, 17) (dual of [(12921, 5), 64475, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹³⁰, 13110, F₂, 5, 17) (dual of [(13110, 5), 65420, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹³⁰, 65550, F₂, 17) (dual of [65550, 65420, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁰, 65553, F₂, 17) (dual of [65553, 65423, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
      1. linear OA(2¹²⁹, 65536, F₂, 17) (dual of [65536, 65407, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(2¹¹³, 65536, F₂, 15) (dual of [65536, 65423, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      3. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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(2¹³⁰, 12920, F₂, 24, 17) (dual of [(12920, 24), 309950, 18]-NRT-code)	[i]		OOA Stacking with Additional Row