MinT - Information on Result #1603619

Information on Result #1603619

Linear OOA(3¹²², 3008, F₃, 4, 23) (dual of [(3008, 4), 11910, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²², 3008, F₃, 2, 23) (dual of [(3008, 2), 5894, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹²², 3285, F₃, 2, 23) (dual of [(3285, 2), 6448, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹²², 6570, F₃, 23) (dual of [6570, 6448, 24]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹²¹, 6569, F₃, 23) (dual of [6569, 6448, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
      1. linear OA(3¹²¹, 6561, F₃, 23) (dual of [6561, 6440, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(3¹¹³, 6561, F₃, 22) (dual of [6561, 6448, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(3⁰, 8, F₃, 0) (dual of [8, 8, 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(3¹²², 1002, F₃, 28, 23) (dual of [(1002, 28), 27934, 24]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row