MinT - Information on Result #2676583

Information on Result #2676583

Linear OOA(3¹⁷⁶, 3327651, F₃, 3, 13) (dual of [(3327651, 3), 9982777, 14]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁷⁵, 3327651, F₃, 3, 13) (dual of [(3327651, 3), 9982778, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁵⁴, 531450, F₃, 3, 6) (dual of [(531450, 3), 1594296, 7]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3⁵⁴, 1594350, F₃, 6) (dual of [1594350, 1594296, 7]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(3) [i] based on
      1. linear OA(3⁵³, 1594323, F₃, 7) (dual of [1594323, 1594270, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3²⁷, 1594323, F₃, 4) (dual of [1594323, 1594296, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3¹, 27, F₃, 1) (dual of [27, 26, 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(3¹²¹, 2796201, F₃, 3, 13) (dual of [(2796201, 3), 8388482, 14]-NRT-code), using
  - OOA 3-folding [i] 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.