MinT - Information on Result #2257897

Information on Result #2257897

Linear OA(2¹¹⁰, 32788, F₂, 14) (dual of [32788, 32678, 15]-code), using 4 times code embedding in larger space based on linear OA(2¹⁰⁶, 32784, F₂, 14) (dual of [32784, 32678, 15]-code), using

1 times truncation [i] based on linear OA(2¹⁰⁷, 32785, F₂, 15) (dual of [32785, 32678, 16]-code), using
- constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
  1. linear OA(2¹⁰⁶, 32768, F₂, 15) (dual of [32768, 32662, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  2. linear OA(2⁹¹, 32768, F₂, 13) (dual of [32768, 32677, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
    - strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
      - dual of repetition code with length 17 [i]
  4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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(2¹¹⁰, 4684, F₂, 7, 14) (dual of [(4684, 7), 32678, 15]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2¹¹⁰, 4684, F₂, 8, 14) (dual of [(4684, 8), 37362, 15]-NRT-code)	[i]	OA Folding and Stacking
3	Linear OOA(2¹¹⁰, 4684, F₂, 14, 14) (dual of [(4684, 14), 65466, 15]-NRT-code)	[i]	OA Folding and Stacking