MinT - Information on Result #1081206

Information on Result #1081206

Linear OOA(3²¹⁹, 4194314, F₃, 4, 15) (dual of [(4194314, 4), 16777037, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶¹, 2796200, F₃, 4, 7) (dual of [(2796200, 4), 11184739, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3⁶¹, 8388601, F₃, 7) (dual of [8388601, 8388540, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(3¹⁵⁸, 2097157, F₃, 4, 15) (dual of [(2097157, 4), 8388470, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁸, 7, F₃, 4, 7) (dual of [(7, 4), 20, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,20P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3¹⁵⁰, 2097150, F₃, 4, 15) (dual of [(2097150, 4), 8388450, 16]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3¹⁵⁰, 8388600, F₃, 15) (dual of [8388600, 8388450, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.