MinT - Information on Result #1696967

Information on Result #1696967

Linear OOA(2⁹⁹, 1337, F₂, 8, 16) (dual of [(1337, 8), 10597, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁹⁹, 1337, F₂, 3, 16) (dual of [(1337, 3), 3912, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁹⁹, 1370, F₂, 3, 16) (dual of [(1370, 3), 4011, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁹⁹, 4110, F₂, 16) (dual of [4110, 4011, 17]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2⁹⁷, 4108, F₂, 16) (dual of [4108, 4011, 17]-code), using
    - 1 times truncation [i] based on linear OA(2⁹⁸, 4109, F₂, 17) (dual of [4109, 4011, 18]-code), using
      - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
        linear OA(2⁹⁷, 4096, F₂, 17) (dual of [4096, 3999, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(2⁸⁵, 4096, F₂, 15) (dual of [4096, 4011, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 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: 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		This result only	Method
1	Linear OOA(2⁹⁹, 1336, F₂, 24, 16) (dual of [(1336, 24), 31965, 17]-NRT-code)	[i]		OOA Stacking with Additional Row