MinT - Information on Result #1663484

Information on Result #1663484

Linear OOA(2¹²¹, 7799, F₂, 6, 16) (dual of [(7799, 6), 46673, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²¹, 7799, F₂, 4, 16) (dual of [(7799, 4), 31075, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹²¹, 8195, F₂, 4, 16) (dual of [(8195, 4), 32659, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹²¹, 32780, F₂, 16) (dual of [32780, 32659, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹²¹, 32783, F₂, 16) (dual of [32783, 32662, 17]-code), using
    - 1 times truncation [i] 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
        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]
        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]
        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: 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

None.