MinT - Information on Result #1059874

Information on Result #1059874

Linear OOA(3¹⁴⁷, 2097336, F₃, 4, 13) (dual of [(2097336, 4), 8389197, 14]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁴⁷, 4194672, F₃, 2, 13) (dual of [(4194672, 2), 8389197, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁶, 371, F₃, 2, 6) (dual of [(371, 2), 716, 7]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²⁶, 742, F₃, 6) (dual of [742, 716, 7]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(3) [i] based on
      1. linear OA(3²⁵, 729, F₃, 7) (dual of [729, 704, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3¹³, 729, F₃, 4) (dual of [729, 716, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 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, 4194301, F₃, 2, 13) (dual of [(4194301, 2), 8388481, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹²¹, 8388602, F₃, 13) (dual of [8388602, 8388481, 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.