The poset metrics that allow binary codes of codimension m to be m-, (m - 1)-, or (m - 2)-perfect

Kim, Hyun Kwang; Krotov, Denis S.

doi:10.1109/isit.2007.4557414

Cited by 6 publications

(5 citation statements)

References 4 publications

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“…The fact that there are relatively many codes with such properties is what first attracted the attention to poset metrics. For perfect or MDS codes with poset metrics see [9,47,53,49,24,72] and [48], among others.…”

Section: )mentioning

confidence: 99%

Alternative Metrics

Firer

2019

Preprint

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Section: )mentioning

confidence: 99%

Alternative Metrics

Firer

2019

Preprint

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“…Since then, the poset metrics gained attention and has been extensively studied in the literature in the context of coding theory, exploring all its major aspects and invariants: MacWilliams Identity ( [6], [12]), perfect and MDS codes [3], [10], [11], duality, packing, and covering problems [13], [15], [16]. Some generalizations of poset metrics were introduced over the years, including its extension to Frobenius and finite principal ideal rings [4], [9] and the poset-block metrics [1].…”

Section: Introductionmentioning

confidence: 99%

Metrics Based on Finite Directed Graphs and Coding Invariants

Etzion

Firer

Machado

2018

IEEE Trans. Inform. Theory

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Given a finite directed graph with n vertices, we define a metric d G on F n q , where F q is the finite field with q elements. The weight of a word is defined as the number of vertices that can be reached by a directed path starting at the support of the vector. Two canonical forms, which do not affect the metric, are given to each graph. Based on these forms we characterize each such metric. We further use these forms to prove that two graphs with different canonical forms yield different metrics. Efficient algorithms to check if a set of metric weights define a metric based on a graph are given. We provide tight bounds on the number of metric weights required to reconstruct the metric. Furthermore, we give a complete description of the group of linear isometries of the graph metrics and a characterization of the graphs for which every linear code admits a G-canonical decomposition. Considering those graphs, we are able to derive an expression of the packing radius of linear codes in such metric spaces. Finally, given a directed graph which determines a hierarchical poset, we present sufficient and necessary conditions to ensure the validity of the MacWilliams Identity and the MacWilliams Extension Property. i 0, then w(x) ≤ w(x ′ ).

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“…Veterinary drugs are commonly used in pig management and production; for instance, the antiparasitic agent thiophanate has been used for in-feed medication to reduce the migration of Ascaris suum larvae [6], thereby improving both health and performance of pigs. Yohimbine, an ␣ 2 -adrenergic receptor antagonist, can reverse the anesthetic effect of tiletamine-zolazepam and xylazine or of xylazine, ketamine, and telazol, administered simultaneously in sows [7,8]; consequently, the physiological parameters return to normal homeostatic ranges more quickly. Postweaning altrenogest treatment has been found to improve the ovulation rate, farrowing rate, embryo survival rate, and litter size [9,10].…”

Section: Introductionmentioning

confidence: 99%

Determination of residual levels of naloxone, yohimbine, thiophanate, and altrenogest in porcine muscle using QuEChERS with liquid chromatography and triple quadrupole mass spectrometry

Zhang

Park

Kim

et al. 2016

J of Separation Science

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A quick, easy, cheap, effective, rugged, and safe QuEChERS (method) was used for the simultaneous detection of four veterinary drug residues, namely naloxone, yohimbine, thiophanate, and altrenogest, in porcine muscle, using liquid chromatography with electrospray ionization triple quadrupole tandem mass spectrometry. Because of the unavailability of a suitable internal standard, matrix-matched calibrations were used for quantification, with determination coefficients ≥ 0.9542. The accuracy (expressed as recovery %) ranged from 60.53 to 83.25%, and the intra- and interday precisions (expressed as relative standard deviations) were <12%. The limits of quantification were 5, 0.5, 2, and 5 ng/g for naloxone, yohimbine, thiophanate, and altrenogest, respectively. Samples purchased from local markets in Seoul, Republic of Korea, revealed no traces of the target analytes. The developed method described herein is sensitive and reliable and can be applied to quantify the tested veterinary drugs in animal tissues.

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The poset metrics that allow binary codes of codimension m to be m-, (m - 1)-, or (m - 2)-perfect

Cited by 6 publications

References 4 publications

Alternative Metrics

Alternative Metrics

Metrics Based on Finite Directed Graphs and Coding Invariants

Determination of residual levels of naloxone, yohimbine, thiophanate, and altrenogest in porcine muscle using QuEChERS with liquid chromatography and triple quadrupole mass spectrometry

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