MinT - Information on Result #1778014

Information on Result #1778014

Digital (151, 174, 416759)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁷⁴, 416759, F₄, 2, 23) (dual of [(416759, 2), 833344, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁷⁴, 524299, F₄, 2, 23) (dual of [(524299, 2), 1048424, 24]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁷³, 524299, F₄, 2, 23) (dual of [(524299, 2), 1048425, 24]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁷³, 1048598, F₄, 23) (dual of [1048598, 1048425, 24]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4¹⁷², 1048597, F₄, 23) (dual of [1048597, 1048425, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
        linear OA(4¹⁷¹, 1048576, F₄, 23) (dual of [1048576, 1048405, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(4¹⁵¹, 1048576, F₄, 21) (dual of [1048576, 1048425, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(4¹, 21, F₄, 1) (dual of [21, 20, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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.