MinT - Information on Result #2798200

Information on Result #2798200

Linear OOA(3²²⁹, 2391514, F₃, 4, 17) (dual of [(2391514, 4), 9565827, 18]-NRT-code), using 3¹ times duplication based on linear OOA(3²²⁸, 2391514, F₃, 4, 17) (dual of [(2391514, 4), 9565828, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁴, 22, F₃, 4, 8) (dual of [(22, 4), 74, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 14, 22)-net over F₃, using
    - linear code embedding found in a computer search [i]
2. linear OOA(3²¹⁴, 2391492, F₃, 4, 17) (dual of [(2391492, 4), 9565754, 18]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(3²¹⁴, 4782984, F₃, 2, 17) (dual of [(4782984, 2), 9565754, 18]-NRT-code), using
    - trace code [i] based on linear OOA(9¹⁰⁷, 2391492, F₉, 2, 17) (dual of [(2391492, 2), 4782877, 18]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(9¹⁰⁷, 4782984, F₉, 17) (dual of [4782984, 4782877, 18]-code), using
        constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
        linear OA(9¹⁰⁶, 4782969, F₉, 17) (dual of [4782969, 4782863, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(9¹, 15, F₉, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.