MinT - Information on Result #1714922

Information on Result #1714922

Digital (122, 144, 6562)-net over F₃, using net defined by OOA based on linear OOA(3¹⁴⁴, 6562, F₃, 28, 22) (dual of [(6562, 28), 183592, 23]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(3¹⁴⁴, 19687, F₃, 4, 22) (dual of [(19687, 4), 78604, 23]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁴⁴, 19687, F₃, 3, 22) (dual of [(19687, 3), 58917, 23]-NRT-code), using
  - 3¹ times duplication [i] based on linear OOA(3¹⁴³, 19687, F₃, 3, 22) (dual of [(19687, 3), 58918, 23]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3¹⁴³, 59061, F₃, 22) (dual of [59061, 58918, 23]-code), using
      - 1 times code embedding in larger space [i] based on linear OA(3¹⁴², 59060, F₃, 22) (dual of [59060, 58918, 23]-code), using
        constructionÂ X applied to C_e(21) âŠ‚ C_e(19) [i] based on
        linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(3¹³¹, 59049, F₃, 20) (dual of [59049, 58918, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
        linear OA(3¹, 11, F₃, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.