MinT - Information on Result #945596

Information on Result #945596

Linear OOA(2⁹⁹, 1370, F₂, 3, 16) (dual of [(1370, 3), 4011, 17]-NRT-code), using OOA 3-folding based on linear OA(2⁹⁹, 4110, F₂, 16) (dual of [4110, 4011, 17]-code), using

2 times code embedding in larger space [i] based on linear OA(2⁹⁷, 4108, F₂, 16) (dual of [4108, 4011, 17]-code), using
- 1 times truncation [i] based on linear OA(2⁹⁸, 4109, F₂, 17) (dual of [4109, 4011, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
    1. linear OA(2⁹⁷, 4096, F₂, 17) (dual of [4096, 3999, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(2⁸⁵, 4096, F₂, 15) (dual of [4096, 4011, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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(2¹⁰⁰, 1370, F₂, 3, 16) (dual of [(1370, 3), 4010, 17]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁰¹, 1370, F₂, 3, 16) (dual of [(1370, 3), 4009, 17]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2⁹⁹, 1337, F₂, 4, 16) (dual of [(1337, 4), 5249, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2⁹⁹, 1337, F₂, 5, 16) (dual of [(1337, 5), 6586, 17]-NRT-code)	[i]
5	Linear OOA(2⁹⁹, 1337, F₂, 6, 16) (dual of [(1337, 6), 7923, 17]-NRT-code)	[i]
6	Linear OOA(2⁹⁹, 1337, F₂, 7, 16) (dual of [(1337, 7), 9260, 17]-NRT-code)	[i]
7	Linear OOA(2⁹⁹, 1337, F₂, 8, 16) (dual of [(1337, 8), 10597, 17]-NRT-code)	[i]
8	Digital (83, 99, 1337)-net over F₂	[i]