MinT - Information on Result #895573

Information on Result #895573

Linear OOA(4¹⁶⁴, 4196352, F₄, 2, 15) (dual of [(4196352, 2), 8392540, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4³¹, 2051, F₄, 2, 7) (dual of [(2051, 2), 4071, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4³¹, 4102, F₄, 7) (dual of [4102, 4071, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(4³¹, 4096, F₄, 7) (dual of [4096, 4065, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(4²⁵, 4096, F₄, 6) (dual of [4096, 4071, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    3. linear OA(4⁰, 6, F₄, 0) (dual of [6, 6, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(4¹³³, 4194301, F₄, 2, 15) (dual of [(4194301, 2), 8388469, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹³³, 8388602, F₄, 15) (dual of [8388602, 8388469, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹³³, large, F₄, 15) (dual of [large, large−133, 16]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.