MinT - Information on Result #2480638

Information on Result #2480638

Linear OOA(2²⁵⁷, 2056, F₂, 2, 42) (dual of [(2056, 2), 3855, 43]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(2²⁵³, 2054, F₂, 2, 42) (dual of [(2054, 2), 3855, 43]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²⁵³, 4108, F₂, 42) (dual of [4108, 3855, 43]-code), using
- 1 times truncation [i] based on linear OA(2²⁵⁴, 4109, F₂, 43) (dual of [4109, 3855, 44]-code), using
  - constructionÂ X applied to C_e(42) âŠ‚ C_e(40) [i] based on
    1. linear OA(2²⁵³, 4096, F₂, 43) (dual of [4096, 3843, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
    2. linear OA(2²⁴¹, 4096, F₂, 41) (dual of [4096, 3855, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
    3. linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 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(2²⁵⁷, 1375, F₂, 3, 42) (dual of [(1375, 3), 3868, 43]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁷, 1375, F₂, 4, 42) (dual of [(1375, 4), 5243, 43]-NRT-code)	[i]
3	Linear OOA(2²⁵⁷, 1375, F₂, 5, 42) (dual of [(1375, 5), 6618, 43]-NRT-code)	[i]
4	Linear OOA(2²⁵⁷, 1375, F₂, 6, 42) (dual of [(1375, 6), 7993, 43]-NRT-code)	[i]
5	Linear OOA(2²⁵⁷, 1375, F₂, 7, 42) (dual of [(1375, 7), 9368, 43]-NRT-code)	[i]
6	Linear OOA(2²⁵⁷, 1375, F₂, 8, 42) (dual of [(1375, 8), 10743, 43]-NRT-code)	[i]
7	Digital (215, 257, 1375)-net over F₂	[i]