MinT - Information on Result #1059987

Information on Result #1059987

Linear OOA(3¹⁶⁸, 2097700, F₃, 4, 14) (dual of [(2097700, 4), 8390632, 15]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁶⁸, 4195400, F₃, 2, 14) (dual of [(4195400, 2), 8390632, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁸, 4195401, F₃, 2, 14) (dual of [(4195401, 2), 8390634, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3³², 1100, F₃, 2, 7) (dual of [(1100, 2), 2168, 8]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3³², 2200, F₃, 7) (dual of [2200, 2168, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(3) [i] based on
        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]
        linear OA(3¹⁵, 2187, F₃, 4) (dual of [2187, 2172, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
  2. linear OOA(3¹³⁶, 4194301, F₃, 2, 14) (dual of [(4194301, 2), 8388466, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹³⁶, 8388602, F₃, 14) (dual of [8388602, 8388466, 15]-code), using
      - discarding factors / shortening the dual code 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.