MinT - Information on Result #1080994

Information on Result #1080994

Linear OOA(3¹²⁵, 2097517, F₃, 4, 11) (dual of [(2097517, 4), 8389943, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 367, F₃, 4, 5) (dual of [(367, 4), 1449, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3¹⁹, 735, F₃, 5) (dual of [735, 716, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(3¹⁹, 729, F₃, 5) (dual of [729, 710, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3⁰, 6, F₃, 0) (dual of [6, 6, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(3¹⁰⁶, 2097150, F₃, 4, 11) (dual of [(2097150, 4), 8388494, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁰⁶, 8388600, F₃, 11) (dual of [8388600, 8388494, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.