MinT - Information on Result #2221175

Information on Result #2221175

Linear OA(2¹⁰⁶, 135, F₂, 44) (dual of [135, 29, 45]-code), using 1 times truncation based on linear OA(2¹⁰⁷, 136, F₂, 45) (dual of [136, 29, 46]-code), using

constructionÂ X applied to C_e(46) âŠ‚ C_e(42) [i] based on
1. linear OA(2¹⁰⁶, 128, F₂, 47) (dual of [128, 22, 48]-code), using an extension C_e(46) of the primitive narrow-sense BCH-code C(I) with length 127Â = 2⁷âˆ’1, defining interval IÂ =Â [1,46], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 47 [i]
2. linear OA(2⁹⁹, 128, F₂, 43) (dual of [128, 29, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 127Â = 2⁷âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
3. linear OA(2¹, 8, F₂, 1) (dual of [8, 7, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(2¹¹², 141, F₂, 44) (dual of [141, 29, 45]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2¹¹³, 142, F₂, 44) (dual of [142, 29, 45]-code)	[i]
3	Linear OA(2¹¹⁴, 143, F₂, 44) (dual of [143, 29, 45]-code)	[i]
4	Linear OA(2¹¹⁶, 146, F₂, 44) (dual of [146, 30, 45]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OA(2¹²¹, 152, F₂, 44) (dual of [152, 31, 45]-code)	[i]
6	Linear OA(2¹²⁴, 156, F₂, 44) (dual of [156, 32, 45]-code)	[i]
7	Linear OOA(2¹⁰⁶, 67, F₂, 2, 44) (dual of [(67, 2), 28, 45]-NRT-code)	[i]	OOA Folding
8	Linear OOA(2¹⁰⁶, 45, F₂, 3, 44) (dual of [(45, 3), 29, 45]-NRT-code)	[i]
9	Linear OOA(2¹⁰⁶, 27, F₂, 5, 44) (dual of [(27, 5), 29, 45]-NRT-code)	[i]