MinT - Information on Result #1051716

Information on Result #1051716

Linear OOA(2¹²², 32773, F₂, 4, 15) (dual of [(32773, 4), 130970, 16]-NRT-code), using OOA 4-folding based on linear OA(2¹²², 131092, F₂, 15) (dual of [131092, 130970, 16]-code), using

1 times code embedding in larger space [i] based on linear OA(2¹²¹, 131091, F₂, 15) (dual of [131091, 130970, 16]-code), using
- constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
  1. linear OA(2¹²⁰, 131072, F₂, 15) (dual of [131072, 130952, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  2. 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]
  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(2¹²³, 32773, F₂, 4, 15) (dual of [(32773, 4), 130969, 16]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹²⁴, 32773, F₂, 4, 15) (dual of [(32773, 4), 130968, 16]-NRT-code)	[i]
3	Linear OOA(2¹²⁵, 32773, F₂, 4, 15) (dual of [(32773, 4), 130967, 16]-NRT-code)	[i]