MinT - Information on Result #1671147

Information on Result #1671147

Linear OOA(2²⁴⁴, 1285, F₂, 6, 41) (dual of [(1285, 6), 7466, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁴, 1285, F₂, 3, 41) (dual of [(1285, 3), 3611, 42]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁴, 1370, F₂, 3, 41) (dual of [(1370, 3), 3866, 42]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²⁴³, 1370, F₂, 3, 41) (dual of [(1370, 3), 3867, 42]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁴³, 4110, F₂, 41) (dual of [4110, 3867, 42]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2²⁴², 4109, F₂, 41) (dual of [4109, 3867, 42]-code), using
      - constructionÂ X applied to C_e(40) âŠ‚ C_e(38) [i] based on
        linear OA(2²⁴¹, 4096, F₂, 41) (dual of [4096, 3855, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
        linear OA(2²²⁹, 4096, F₂, 39) (dual of [4096, 3867, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [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

None.