MinT - Information on Result #2224187

Information on Result #2224187

Linear OA(2¹²¹, 32783, F₂, 16) (dual of [32783, 32662, 17]-code), using 1 times truncation based on linear OA(2¹²², 32784, F₂, 17) (dual of [32784, 32662, 18]-code), using

constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
1. linear OA(2¹²¹, 32768, F₂, 17) (dual of [32768, 32647, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
2. 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]
3. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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(2¹²¹, 16391, F₂, 2, 16) (dual of [(16391, 2), 32661, 17]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2¹²¹, 10927, F₂, 3, 16) (dual of [(10927, 3), 32660, 17]-NRT-code)	[i]
3	Linear OOA(2¹²¹, 8195, F₂, 4, 16) (dual of [(8195, 4), 32659, 17]-NRT-code)	[i]
4	Linear OOA(2¹²¹, 6556, F₂, 5, 16) (dual of [(6556, 5), 32659, 17]-NRT-code)	[i]
5	Linear OOA(2¹²¹, 5463, F₂, 6, 16) (dual of [(5463, 6), 32657, 17]-NRT-code)	[i]
6	Linear OOA(2¹²¹, 4683, F₂, 7, 16) (dual of [(4683, 7), 32660, 17]-NRT-code)	[i]
7	Linear OOA(2¹²¹, 4097, F₂, 8, 16) (dual of [(4097, 8), 32655, 17]-NRT-code)	[i]
8	Linear OOA(2¹²¹, 4097, F₂, 16, 16) (dual of [(4097, 16), 65431, 17]-NRT-code)	[i]	OA Folding and Stacking