MinT - Information on Result #1097125

Information on Result #1097125

Linear OOA(2²⁴¹, 6556, F₂, 5, 32) (dual of [(6556, 5), 32539, 33]-NRT-code), using OOA 5-folding based on linear OA(2²⁴¹, 32780, F₂, 32) (dual of [32780, 32539, 33]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁴¹, 32783, F₂, 32) (dual of [32783, 32542, 33]-code), using
- 1 times truncation [i] based on linear OA(2²⁴², 32784, F₂, 33) (dual of [32784, 32542, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(30) [i] based on
    1. linear OA(2²⁴¹, 32768, F₂, 33) (dual of [32768, 32527, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(2²²⁶, 32768, F₂, 31) (dual of [32768, 32542, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    3. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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(2²⁴¹, 5660, F₂, 6, 32) (dual of [(5660, 6), 33719, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴¹, 5660, F₂, 7, 32) (dual of [(5660, 7), 39379, 33]-NRT-code)	[i]
3	Linear OOA(2²⁴¹, 5660, F₂, 8, 32) (dual of [(5660, 8), 45039, 33]-NRT-code)	[i]
4	Digital (209, 241, 5660)-net over F₂	[i]