MinT - Information on Result #1096383

Information on Result #1096383

Linear OOA(2¹⁹⁶, 13111, F₂, 5, 24) (dual of [(13111, 5), 65359, 25]-NRT-code), using OOA 5-folding based on linear OA(2¹⁹⁶, 65555, F₂, 24) (dual of [65555, 65359, 25]-code), using

3 times code embedding in larger space [i] based on linear OA(2¹⁹³, 65552, F₂, 24) (dual of [65552, 65359, 25]-code), using
- 1 times truncation [i] based on linear OA(2¹⁹⁴, 65553, F₂, 25) (dual of [65553, 65359, 26]-code), using
  - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
    1. linear OA(2¹⁹³, 65536, F₂, 25) (dual of [65536, 65343, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    2. linear OA(2¹⁷⁷, 65536, F₂, 23) (dual of [65536, 65359, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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: Constructive and 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		Method
1	Linear OOA(2¹⁹⁷, 13111, F₂, 5, 24) (dual of [(13111, 5), 65358, 25]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁹⁶, 11788, F₂, 6, 24) (dual of [(11788, 6), 70532, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁹⁶, 11788, F₂, 7, 24) (dual of [(11788, 7), 82320, 25]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁶, 11788, F₂, 8, 24) (dual of [(11788, 8), 94108, 25]-NRT-code)	[i]
5	Digital (172, 196, 11788)-net over F₂	[i]