MinT - Information on Result #2257748

Information on Result #2257748

Linear OA(2¹⁰⁸, 131095, F₂, 13) (dual of [131095, 130987, 14]-code), using 4 times code embedding in larger space based on linear OA(2¹⁰⁴, 131091, F₂, 13) (dual of [131091, 130987, 14]-code), using

constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
1. linear OA(2¹⁰³, 131072, F₂, 13) (dual of [131072, 130969, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
2. linear OA(2⁸⁶, 131072, F₂, 11) (dual of [131072, 130986, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
3. linear OA(2¹⁸, 19, F₂, 17) (dual of [19, 1, 18]-code), using
  - strength reduction [i] based on linear OA(2¹⁸, 19, F₂, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
    - dual of repetition code with length 19 [i]
4. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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(2¹⁰⁸, 26219, F₂, 5, 13) (dual of [(26219, 5), 130987, 14]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2¹⁰⁸, 21849, F₂, 7, 13) (dual of [(21849, 7), 152835, 14]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row
3	Linear OOA(2¹⁰⁸, 21849, F₂, 8, 13) (dual of [(21849, 8), 174684, 14]-NRT-code)	[i]
4	Linear OOA(2¹⁰⁸, 21849, F₂, 13, 13) (dual of [(21849, 13), 283929, 14]-NRT-code)	[i]