MinT - Information on Result #1010970

Information on Result #1010970

Linear OOA(3²³⁴, 2796446, F₃, 3, 20) (dual of [(2796446, 3), 8389104, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁸, 245, F₃, 3, 10) (dual of [(245, 3), 697, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3³⁸, 735, F₃, 10) (dual of [735, 697, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³⁸, 736, F₃, 10) (dual of [736, 698, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(7) [i] based on
      1. linear OA(3³⁷, 729, F₃, 10) (dual of [729, 692, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(3³¹, 729, F₃, 8) (dual of [729, 698, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(3¹, 7, F₃, 1) (dual of [7, 6, 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]
linear OOA(3¹⁹⁶, 2796201, F₃, 3, 20) (dual of [(2796201, 3), 8388407, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁹⁶, large, F₃, 20) (dual of [large, large−196, 21]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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.