MinT - Information on Result #1650118

Information on Result #1650118

Linear OOA(3²²³, 398584, F₃, 5, 26) (dual of [(398584, 5), 1992697, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²³, 398584, F₃, 4, 26) (dual of [(398584, 4), 1594113, 27]-NRT-code), using

3¹ times duplication [i] based on linear OOA(3²²², 398584, F₃, 4, 26) (dual of [(398584, 4), 1594114, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3²²², 1594336, F₃, 26) (dual of [1594336, 1594114, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
    1. linear OA(3²²², 1594323, F₃, 26) (dual of [1594323, 1594101, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(3²⁰⁹, 1594323, F₃, 25) (dual of [1594323, 1594114, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(3⁰, 13, F₃, 0) (dual of [13, 13, 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]

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, 398584, F₃, 5, 26) (dual of [(398584, 5), 1992696, 27]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²²⁵, 398584, F₃, 5, 26) (dual of [(398584, 5), 1992695, 27]-NRT-code)	[i]		OOA Duplication
3	Linear OOA(3²²³, 132861, F₃, 35, 26) (dual of [(132861, 35), 4649912, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row