MinT - Information on Result #2266713

Information on Result #2266713

Linear OA(3¹⁶⁹, 794, F₃, 38) (dual of [794, 625, 39]-code), using 1 times code embedding in larger space based on linear OA(3¹⁶⁸, 793, F₃, 38) (dual of [793, 625, 39]-code), using

constructionÂ XX applied to C₁Â =Â C([722,25]), C₂Â =Â C([0,31]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,25]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([722,31]) [i] based on
1. linear OA(3¹²⁷, 728, F₃, 32) (dual of [728, 601, 33]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,25}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
2. linear OA(3¹²⁴, 728, F₃, 32) (dual of [728, 604, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
3. linear OA(3¹⁴⁸, 728, F₃, 38) (dual of [728, 580, 39]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,31}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
4. linear OA(3¹⁰³, 728, F₃, 26) (dual of [728, 625, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
5. linear OA(3¹⁰, 34, F₃, 5) (dual of [34, 24, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 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 OA(3³, 12, F₃, 2) (dual of [12, 9, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
      3. linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
        extended Golay code G_e(3) [i]
6. linear OA(3¹⁰, 31, F₃, 5) (dual of [31, 21, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code) (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁶⁹, 397, F₃, 2, 38) (dual of [(397, 2), 625, 39]-NRT-code)	[i]		OOA Folding