MinT - Information on Result #1784631

Information on Result #1784631

Digital (220, 253, 437400)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²⁵³, 437400, F₄, 2, 33) (dual of [(437400, 2), 874547, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²⁵³, 524314, F₄, 2, 33) (dual of [(524314, 2), 1048375, 34]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²⁵², 524314, F₄, 2, 33) (dual of [(524314, 2), 1048376, 34]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁵², 1048628, F₄, 33) (dual of [1048628, 1048376, 34]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4²⁵¹, 1048627, F₄, 33) (dual of [1048627, 1048376, 34]-code), using
      - constructionÂ X applied to C([0,16]) âŠ‚ C([0,13]) [i] based on
        linear OA(4²⁴¹, 1048577, F₄, 33) (dual of [1048577, 1048336, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
        linear OA(4²⁰¹, 1048577, F₄, 27) (dual of [1048577, 1048376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
        linear OA(4¹⁰, 50, F₄, 5) (dual of [50, 40, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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.