MinT - Information on Result #1651309

Information on Result #1651309

Linear OOA(3²³⁶, 511627, F₃, 5, 26) (dual of [(511627, 5), 2557899, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³⁶, 511627, F₃, 3, 26) (dual of [(511627, 3), 1534645, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³⁶, 531463, F₃, 3, 26) (dual of [(531463, 3), 1594153, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3²³³, 531462, F₃, 3, 26) (dual of [(531462, 3), 1594153, 27]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²³³, 1594386, F₃, 26) (dual of [1594386, 1594153, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(19) [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(3¹⁷⁰, 1594323, F₃, 20) (dual of [1594323, 1594153, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(3¹¹, 63, F₃, 5) (dual of [63, 52, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3²³⁶, 170542, F₃, 35, 26) (dual of [(170542, 35), 5968734, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row