Results 31 to 40 of about 10,192,265 (264)
Information and Control, 1972 A cyclic code over a finite field may be viewed as an ideal in the group algebra of a cyclic group over a finite field. As a possible extension to this case the paper considers linear cyclic codes over the residue ring of integers \(\mathbb Z_m\) as ideals in the group ring \(\mathbb Z_nC_n\). The group ring is semisimple if and only if \((m,n)=1\) and
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Linear Codes over Finite Chain Rings [PDF]
The Electronic Journal of Combinatorics, 1999 The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a well-known result for linear codes over fields, we prove that there exists a one-to-one correspondence between so-called fat linear codes over chain rings and multisets of points in projective Hjelmslev geometries, in the ...
Thomas Honold, Ivan N. Landjev
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Therapeutic Apheresis and Dialysis, EarlyView.ABSTRACT Background Chronic micro‐inflammation in patients with end‐stage renal disease (ESRD) is a significant driver of cardiovascular complications and diminished quality of life. While standard hemodialysis (SHD) effectively manages small‐molecule clearance, its ability to remove medium‐to‐large uremic toxins—the primary catalysts of systemic ...
Hongwei Zuo +5 more
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MacWilliams Identities and Generator Matrices for Linear Codes over ℤp4[u]/(u2 − p3β, pu)
AxiomsSuppose that R=Zp4[u] with u2=p3β and pu=0, where p is a prime and β is a unit in R. Then, R is a local non-chain ring of order p5 with a unique maximal ideal J=(p,u) and a residue field of order p. A linear code C of length N over R is an R-submodule of
Sami Alabiad +2 more
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On the equivalence of codes over rings and modules
Finite Fields and Their Applications, 2004 One of the foundational results of algebraic coding theory is the MacWilliams equivalence theorem. Wood has generalized this result to show that for finite Frobenius rings a generalization of the result holds. Determining what the class of rings to which the theorem will generalize remains an open question. The authors define a ring to be a MacWilliams
Hai Quang Dinh 0001 +1 more
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, 2002 The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all ...
Vasantha, Kandasamy
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Therapeutic Apheresis and Dialysis, EarlyView.ABSTRACT Introduction This final analysis of a multicenter, prospective postmarketing surveillance study evaluated the safety of daprodustat in patients with chronic kidney disease anemia in routine clinical practice in Japan. Methods Patients who initiated daprodustat between September 2020 and July 2022 were registered.
Tadao Akizawa +7 more
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On Linear Codes over Local Rings of Order p4
MathematicsSuppose R is a local ring with invariants p,n,r,m,k and mr=4, that is R of order p4. Then, R=R0+uR0+vR0+wR0 has maximal ideal J=uR0+vR0+wR0 of order p(m−1)r and a residue field F of order pr, where R0=GR(pn,r) is the coefficient subring of R.
Sami Alabiad +2 more
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Terahertz Metalens for Multifocusing Bidirectional Arrangement in Different Dimensions
IEEE Photonics Journal, 2019 Metasurface lenses are typically investigated for a lot of characteristics, but the design method for conventional devices is comparatively simple in terms of controlling the quantity, position, and size of focal spots.
Jicheng Wang +4 more
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Therapeutic Apheresis and Dialysis, EarlyView.ABSTRACT Introduction Peritoneal dialysis (PD) is an established home‐based kidney replacement therapy (KRT), but its uptake remains low in Japan. We evaluated whether individualized education in a dedicated outpatient clinic was associated with the initiation of PD.
Yasuko Ito +7 more
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