MinT - Information on Result #1131320

Information on Result #1131320

Linear OOA(2¹⁶⁹, 349529, F₂, 6, 16) (dual of [(349529, 6), 2097005, 17]-NRT-code), using OOA 6-folding based on linear OA(2¹⁶⁹, 2097174, F₂, 16) (dual of [2097174, 2097005, 17]-code), using

1 times truncation [i] based on linear OA(2¹⁷⁰, 2097175, F₂, 17) (dual of [2097175, 2097005, 18]-code), using
- constructionÂ X4 applied to C_e(16) âŠ‚ C_e(14) [i] based on
  1. linear OA(2¹⁶⁹, 2097152, F₂, 17) (dual of [2097152, 2096983, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  2. 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]
  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 OOA(2¹⁷¹, 349529, F₂, 6, 16) (dual of [(349529, 6), 2097003, 17]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁷², 349529, F₂, 6, 16) (dual of [(349529, 6), 2097002, 17]-NRT-code)	[i]
3	Linear OOA(2¹⁷³, 349529, F₂, 6, 16) (dual of [(349529, 6), 2097001, 17]-NRT-code)	[i]