Results 11 to 20 of about 143,950 (277)
Codes over Matrix Rings for Space-Time Coded Modulations [PDF]
IEEE Transactions on Information Theory, 2010 It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an ...
Belfiore, Jean-Claude +2 more
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Linear Codes over Finite Rings
Trends in Computational and Applied Mathematics, 2005 In this paper we present a construction technique of cyclic, BCH, alternat, Goppa and Srivastava codes over a local finite commutative rings with identity.
A.A. de Andrade, R. Palazzo Jr.
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Some Constacyclic Codes over Finite Chain Rings [PDF]
Advances in Mathematics of Communications, 2012 For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes.
Batoul, Aicha +2 more
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Skew constacyclic codes over Galois rings
Advances in Mathematics of Communications, 2008 We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied.
Boucher, Delphine +2 more
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On Double Cyclic Codes over Finite Chain Rings for DNA Computing [PDF]
EntropyLet e be a fixed positive integer and n1,n2 be odd positive integers. The main objective of this article is to investigate the algebraic structure of double cyclic codes of length (n1,n2) over the finite chain ring Re = F4e+vF4e, where v2=0.
Shakir Ali +4 more
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On Linear Codes over Finite Singleton Local Rings
MathematicsThe study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings.
Sami Alabiad +2 more
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Skew constacyclic codes over finite chain rings
Advances in Mathematics of Communications, 2012 Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of $x^n- $, where $ $ is a unit element, are exhibited.
Jitman, Somphong +2 more
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IEEE Access, 2023 A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
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On the Covering Radius of Codes over Zpk
Mathematics, 2020 In this correspondence, we investigate the covering radius of various types of repetition codes over Z p k ( k ≥ 2 ) with respect to the Lee distance.
Mohan Cruz +2 more
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Ideal Codes Over Separable Ring Extensions [PDF]
IEEE Transactions on Information Theory, 2017 This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all previously known as well as new non trivial examples.
Jose Gomez-Torrecillas +2 more
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