MinT - Information on Result #2480140

Information on Result #2480140

Linear OOA(2²⁰², 1031, F₂, 2, 36) (dual of [(1031, 2), 1860, 37]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²⁰⁰, 1030, F₂, 2, 36) (dual of [(1030, 2), 1860, 37]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²⁰⁰, 2060, F₂, 36) (dual of [2060, 1860, 37]-code), using
- strength reduction [i] based on linear OA(2²⁰⁰, 2060, F₂, 37) (dual of [2060, 1860, 38]-code), using
  - constructionÂ X applied to C_e(36) âŠ‚ C_e(34) [i] based on
    1. linear OA(2¹⁹⁹, 2048, F₂, 37) (dual of [2048, 1849, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
    2. linear OA(2¹⁸⁸, 2048, F₂, 35) (dual of [2048, 1860, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    3. linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 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(2²⁰², 832, F₂, 3, 36) (dual of [(832, 3), 2294, 37]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰², 832, F₂, 4, 36) (dual of [(832, 4), 3126, 37]-NRT-code)	[i]
3	Linear OOA(2²⁰², 832, F₂, 5, 36) (dual of [(832, 5), 3958, 37]-NRT-code)	[i]
4	Linear OOA(2²⁰², 832, F₂, 6, 36) (dual of [(832, 6), 4790, 37]-NRT-code)	[i]
5	Linear OOA(2²⁰², 832, F₂, 7, 36) (dual of [(832, 7), 5622, 37]-NRT-code)	[i]
6	Linear OOA(2²⁰², 832, F₂, 8, 36) (dual of [(832, 8), 6454, 37]-NRT-code)	[i]
7	Digital (166, 202, 832)-net over F₂	[i]