MinT - Information on Result #2676702

Information on Result #2676702

Linear OOA(3¹⁶⁷, 2796933, F₃, 3, 14) (dual of [(2796933, 3), 8390632, 15]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁶⁶, 2796933, F₃, 3, 14) (dual of [(2796933, 3), 8390633, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3³⁰, 732, F₃, 3, 7) (dual of [(732, 3), 2166, 8]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3³⁰, 2196, F₃, 7) (dual of [2196, 2166, 8]-code), using
    - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(4) [i] based on
      1. linear OA(3²⁹, 2187, F₃, 7) (dual of [2187, 2158, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3²², 2187, F₃, 5) (dual of [2187, 2165, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(3⁸, 9, F₃, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
        dual of repetition code with length 9 [i]
      4. linear OA(3¹, 9, F₃, 1) (dual of [9, 8, 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]
2. linear OOA(3¹³⁶, 2796201, F₃, 3, 14) (dual of [(2796201, 3), 8388467, 15]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹³⁶, large, F₃, 14) (dual of [large, large−136, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.