MinT - Information on Result #1606936

Information on Result #1606936

Linear OOA(3¹⁷⁸, 65587, F₃, 4, 23) (dual of [(65587, 4), 262170, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷⁸, 65587, F₃, 2, 23) (dual of [(65587, 2), 130996, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷⁸, 88601, F₃, 2, 23) (dual of [(88601, 2), 177024, 24]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁷⁷, 88601, F₃, 2, 23) (dual of [(88601, 2), 177025, 24]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁷⁷, 177202, F₃, 23) (dual of [177202, 177025, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(16) [i] based on
      1. linear OA(3¹⁶⁶, 177147, F₃, 23) (dual of [177147, 176981, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(3¹²², 177147, F₃, 17) (dual of [177147, 177025, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(3¹¹, 55, F₃, 5) (dual of [55, 44, 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(3¹⁷⁸, 21862, F₃, 28, 23) (dual of [(21862, 28), 611958, 24]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row