MinT - Information on Result #1540393

Information on Result #1540393

Linear OOA(4¹⁸⁸, 4190771, F₄, 3, 21) (dual of [(4190771, 3), 12572125, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁸⁸, 4190771, F₄, 2, 21) (dual of [(4190771, 2), 8381354, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁸⁸, 4194304, F₄, 2, 21) (dual of [(4194304, 2), 8388420, 22]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁸⁷, 4194304, F₄, 2, 21) (dual of [(4194304, 2), 8388421, 22]-NRT-code), using
  - 3 times NRT-code embedding in larger space [i] based on linear OOA(4¹⁸¹, 4194301, F₄, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(4¹⁸¹, 8388602, F₄, 21) (dual of [8388602, 8388421, 22]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁸¹, large, F₄, 21) (dual of [large, large−181, 22]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(4¹⁸⁸, 1047692, F₄, 27, 21) (dual of [(1047692, 27), 28287496, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row