MinT - Information on Result #1643984

Information on Result #1643984

Linear OOA(3¹³⁸, 68006, F₃, 5, 18) (dual of [(68006, 5), 339892, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁸, 68006, F₃, 2, 18) (dual of [(68006, 2), 135874, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹³⁸, 88587, F₃, 2, 18) (dual of [(88587, 2), 177036, 19]-NRT-code), using
- strength reduction [i] based on linear OOA(3¹³⁸, 88587, F₃, 2, 19) (dual of [(88587, 2), 177036, 20]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹³⁸, 177174, F₃, 19) (dual of [177174, 177036, 20]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹³⁷, 177173, F₃, 19) (dual of [177173, 177036, 20]-code), using
      - constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
        linear OA(3¹³³, 177147, F₃, 19) (dual of [177147, 177014, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(3⁴, 26, F₃, 2) (dual of [26, 22, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3¹³⁸, 34002, F₃, 25, 18) (dual of [(34002, 25), 849912, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row