MinT - Information on Result #2257247

Information on Result #2257247

Linear OA(2⁸³, 65555, F₂, 10) (dual of [65555, 65472, 11]-code), using 2 times code embedding in larger space based on linear OA(2⁸¹, 65553, F₂, 10) (dual of [65553, 65472, 11]-code), using

1 times truncation [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(2⁸³, 13111, F₂, 5, 10) (dual of [(13111, 5), 65472, 11]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2⁸³, 13111, F₂, 6, 10) (dual of [(13111, 6), 78583, 11]-NRT-code)	[i]	OA Folding and Stacking
3	Linear OOA(2⁸³, 13111, F₂, 7, 10) (dual of [(13111, 7), 91694, 11]-NRT-code)	[i]
4	Linear OOA(2⁸³, 13111, F₂, 8, 10) (dual of [(13111, 8), 104805, 11]-NRT-code)	[i]
5	Linear OOA(2⁸³, 13111, F₂, 10, 10) (dual of [(13111, 10), 131027, 11]-NRT-code)	[i]