MinT - Information on Result #1081087

Information on Result #1081087

Linear OOA(3¹⁵⁵, 2099343, F₃, 4, 13) (dual of [(2099343, 4), 8397217, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁴, 2193, F₃, 4, 6) (dual of [(2193, 4), 8738, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3³⁴, 6579, F₃, 6) (dual of [6579, 6545, 7]-code), using
  - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(3) [i] based on
    1. linear OA(3³³, 6561, F₃, 7) (dual of [6561, 6528, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(3¹⁷, 6561, F₃, 4) (dual of [6561, 6544, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(3¹⁷, 18, F₃, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,3)), using
      - dual of repetition code with length 18 [i]
    4. linear OA(3¹, 18, F₃, 1) (dual of [18, 17, 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]
linear OOA(3¹²¹, 2097150, F₃, 4, 13) (dual of [(2097150, 4), 8388479, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹²¹, 8388600, F₃, 13) (dual of [8388600, 8388479, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²¹, large, F₃, 13) (dual of [large, large−121, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.