MinT - Information on Result #2790655

Information on Result #2790655

Linear OOA(2²³⁹, 2052, F₂, 4, 37) (dual of [(2052, 4), 7969, 38]-NRT-code), using 2¹ times duplication based on linear OOA(2²³⁸, 2052, F₂, 4, 37) (dual of [(2052, 4), 7970, 38]-NRT-code), using

OOA 4-folding [i] based on linear OA(2²³⁸, 8208, F₂, 37) (dual of [8208, 7970, 38]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2²³⁶, 8206, F₂, 37) (dual of [8206, 7970, 38]-code), using
  - constructionÂ X applied to C_e(36) âŠ‚ C_e(34) [i] based on
    1. linear OA(2²³⁵, 8192, F₂, 37) (dual of [8192, 7957, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    2. linear OA(2²²², 8192, F₂, 35) (dual of [8192, 7970, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [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: 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(2²³⁹, 2031, F₂, 5, 37) (dual of [(2031, 5), 9916, 38]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁹, 2031, F₂, 6, 37) (dual of [(2031, 6), 11947, 38]-NRT-code)	[i]
3	Linear OOA(2²³⁹, 2031, F₂, 7, 37) (dual of [(2031, 7), 13978, 38]-NRT-code)	[i]
4	Linear OOA(2²³⁹, 2031, F₂, 8, 37) (dual of [(2031, 8), 16009, 38]-NRT-code)	[i]
5	Digital (202, 239, 2031)-net over F₂	[i]