MinT - Information on Result #805657

Information on Result #805657

Linear OOA(2⁵⁸, 1031, F₂, 2, 11) (dual of [(1031, 2), 2004, 12]-NRT-code), using OOA 2-folding based on linear OA(2⁵⁸, 2062, F₂, 11) (dual of [2062, 2004, 12]-code), using

1 times code embedding in larger space [i] based on linear OA(2⁵⁷, 2061, F₂, 11) (dual of [2061, 2004, 12]-code), using
- constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
  1. linear OA(2⁵⁶, 2048, F₂, 11) (dual of [2048, 1992, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(2⁴⁵, 2048, F₂, 9) (dual of [2048, 2003, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  3. linear OA(2¹², 13, F₂, 11) (dual of [13, 1, 12]-code), using
    - strength reduction [i] based on linear OA(2¹², 13, F₂, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
      - dual of repetition code with length 13 [i]
  4. 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(2⁵⁸, 1031, F₂, 2, 10) (dual of [(1031, 2), 2004, 11]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2⁶⁰, 1032, F₂, 2, 11) (dual of [(1032, 2), 2004, 12]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2⁵⁹, 1031, F₂, 2, 11) (dual of [(1031, 2), 2003, 12]-NRT-code)	[i]	OOA Duplication