MinT - Information on Result #2225770

Information on Result #2225770

Linear OA(2¹⁴⁸, 2097174, F₂, 14) (dual of [2097174, 2097026, 15]-code), using 1 times truncation based on linear OA(2¹⁴⁹, 2097175, F₂, 15) (dual of [2097175, 2097026, 16]-code), using

constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
1. linear OA(2¹⁴⁸, 2097152, F₂, 15) (dual of [2097152, 2097004, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
2. linear OA(2¹²⁷, 2097152, F₂, 13) (dual of [2097152, 2097025, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
3. linear OA(2²², 23, F₂, 21) (dual of [23, 1, 22]-code), using
  - strength reduction [i] based on linear OA(2²², 23, F₂, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
    - dual of repetition code with length 23 [i]
4. linear OA(2¹, 23, F₂, 1) (dual of [23, 22, 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 OA(2¹⁵⁰, 2097176, F₂, 14) (dual of [2097176, 2097026, 15]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2¹⁵¹, 2097177, F₂, 14) (dual of [2097177, 2097026, 15]-code)	[i]
3	Linear OA(2¹⁵², 2097178, F₂, 14) (dual of [2097178, 2097026, 15]-code)	[i]
4	Linear OOA(2¹⁴⁸, 1048587, F₂, 2, 14) (dual of [(1048587, 2), 2097026, 15]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2¹⁴⁸, 699058, F₂, 3, 14) (dual of [(699058, 3), 2097026, 15]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁸, 524293, F₂, 4, 14) (dual of [(524293, 4), 2097024, 15]-NRT-code)	[i]
7	Linear OOA(2¹⁴⁸, 419434, F₂, 5, 14) (dual of [(419434, 5), 2097022, 15]-NRT-code)	[i]
8	Linear OOA(2¹⁴⁸, 349529, F₂, 6, 14) (dual of [(349529, 6), 2097026, 15]-NRT-code)	[i]
9	Linear OOA(2¹⁴⁸, 299596, F₂, 7, 14) (dual of [(299596, 7), 2097024, 15]-NRT-code)	[i]
10	Linear OOA(2¹⁴⁸, 299596, F₂, 8, 14) (dual of [(299596, 8), 2396620, 15]-NRT-code)	[i]	OA Folding and Stacking
11	Linear OOA(2¹⁴⁸, 299596, F₂, 14, 14) (dual of [(299596, 14), 4194196, 15]-NRT-code)	[i]	OA Folding and Stacking