MinT - Information on Result #1610693

Information on Result #1610693

Linear OOA(3²²⁴, 20410, F₃, 4, 33) (dual of [(20410, 4), 81416, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²⁴, 20410, F₃, 2, 33) (dual of [(20410, 2), 40596, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²⁴, 29536, F₃, 2, 33) (dual of [(29536, 2), 58848, 34]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²²³, 29536, F₃, 2, 33) (dual of [(29536, 2), 58849, 34]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²²³, 59072, F₃, 33) (dual of [59072, 58849, 34]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3²²², 59071, F₃, 33) (dual of [59071, 58849, 34]-code), using
      - constructionÂ X applied to C([0,16]) âŠ‚ C([0,15]) [i] based on
        linear OA(3²²¹, 59050, F₃, 33) (dual of [59050, 58829, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
        linear OA(3²⁰¹, 59050, F₃, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
        linear OA(3¹, 21, F₃, 1) (dual of [21, 20, 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]

Mode: 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(3²²⁴, 5102, F₃, 36, 33) (dual of [(5102, 36), 183448, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row