MinT - Information on Result #2610721

Information on Result #2610721

Linear OOA(2⁸⁴, 21852, F₂, 3, 10) (dual of [(21852, 3), 65472, 11]-NRT-code), using strength reduction based on linear OOA(2⁸⁴, 21852, F₂, 3, 11) (dual of [(21852, 3), 65472, 12]-NRT-code), using

OOA 3-folding [i] based on linear OA(2⁸⁴, 65556, F₂, 11) (dual of [65556, 65472, 12]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2⁸², 65554, F₂, 11) (dual of [65554, 65472, 12]-code), using
  - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
    1. linear OA(2⁸¹, 65536, F₂, 11) (dual of [65536, 65455, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(2⁶⁵, 65536, F₂, 9) (dual of [65536, 65471, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    3. linear OA(2¹⁷, 18, F₂, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
      - dual of repetition code with length 18 [i]
    4. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 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(2⁸⁴, 21852, F₂, 4, 10) (dual of [(21852, 4), 87324, 11]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁸⁴, 21852, F₂, 5, 10) (dual of [(21852, 5), 109176, 11]-NRT-code)	[i]
3	Linear OOA(2⁸⁴, 21852, F₂, 6, 10) (dual of [(21852, 6), 131028, 11]-NRT-code)	[i]
4	Linear OOA(2⁸⁴, 21852, F₂, 7, 10) (dual of [(21852, 7), 152880, 11]-NRT-code)	[i]
5	Linear OOA(2⁸⁴, 21852, F₂, 8, 10) (dual of [(21852, 8), 174732, 11]-NRT-code)	[i]
6	Digital (74, 84, 21852)-net over F₂	[i]