MinT - Information on Result #895649

Information on Result #895649

Linear OOA(4¹⁹⁵, 4194431, F₄, 2, 19) (dual of [(4194431, 2), 8388667, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁶, 130, F₄, 2, 9) (dual of [(130, 2), 234, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²⁶, 260, F₄, 9) (dual of [260, 234, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁶, 261, F₄, 9) (dual of [261, 235, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(6) [i] based on
      1. linear OA(4²⁵, 256, F₄, 9) (dual of [256, 231, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(4²¹, 256, F₄, 7) (dual of [256, 235, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(4¹, 5, F₄, 1) (dual of [5, 4, 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]
linear OOA(4¹⁶⁹, 4194301, F₄, 2, 19) (dual of [(4194301, 2), 8388433, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁶⁹, 8388602, F₄, 19) (dual of [8388602, 8388433, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁹, large, F₄, 19) (dual of [large, large−169, 20]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [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.