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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Some Results On Arithmetic Codes Of Composite Length, Tai-Yang Hwang, Carlos R.P. Hartmann
Some Results On Arithmetic Codes Of Composite Length, Tai-Yang Hwang, Carlos R.P. Hartmann
Electrical Engineering and Computer Science - Technical Reports
In this paper we present a new upper bound on the minimum distance of binary cyclic arithmetic codes of composite length. Two new classes of binary cyclic codes of composite length are introduced.
Some Results On The Weight Structure Of Cyclic Codes Of Composite Length, Carlos R.P. Hartmann, T. Y. Hwang
Some Results On The Weight Structure Of Cyclic Codes Of Composite Length, Carlos R.P. Hartmann, T. Y. Hwang
Electrical Engineering and Computer Science - Technical Reports
In this work we investigate the weight structure of cyclic codes of composite length n = n1n2, where n1 and n2 are relatively prime. The actual minimum distances of some classes of binary cyclic codes of composite length are derived. For other classes new lower bounds on the minimum distance are obtained. These new lower bounds improve on the BCH bound for a considerable number of binary cyclic codes.
Weight Distributions Of Some Classes Of Binary Cyclic Codes, Carlos R.P. Hartmann, J. R. Riek Jr., Ralph J. Longobardi
Weight Distributions Of Some Classes Of Binary Cyclic Codes, Carlos R.P. Hartmann, J. R. Riek Jr., Ralph J. Longobardi
Electrical Engineering and Computer Science - Technical Reports
Let h1(x)h2(x) be the parity check polynomial of a binary cyclic code. This article presents a formula for decomposing words in the code as sums of multiples of words in the codes whose parity check polynomials are h1(x) and h2(x). This decomposition provides information about the weight distribution of the code.
Generalized Finite-Geometry Codes, Carlos R.P. Hartmann, Luther D. Rudolph
Generalized Finite-Geometry Codes, Carlos R.P. Hartmann, Luther D. Rudolph
Electrical Engineering and Computer Science - Technical Reports
A technique is presented for constructing cyclic codes that retain many of the combinatorial properties of finite-geometry codes, but are often superior to geometry codes. It is shown that L-step orthogonalization is applicable to certain subclasses of these codes.
Decoding By Sequential Code Reduction, Luther D. Rudolph, Carlos R.P. Hartmann
Decoding By Sequential Code Reduction, Luther D. Rudolph, Carlos R.P. Hartmann
Electrical Engineering and Computer Science - Technical Reports
A general decoding method for cyclic codes is presented which gives promise of substantially reducing the complexity of decoders at the cost of a modest increase in decoding time (or delay). Significant reductions in decoder complexity for binary cyclic finite-geometry codes are demonstrated, and two decoding options for the Golay code are presented.
Some Results On The Distance Properties Of Convolutional Codes, Luther D. Rudolph, Alexander Miczo
Some Results On The Distance Properties Of Convolutional Codes, Luther D. Rudolph, Alexander Miczo
Electrical Engineering and Computer Science - Technical Reports
Rate 1/2 binary convolutional codes are analyzed and a lower bound on free distance in terms of the minimum distances of two associated cyclic codes ìs derived. Next, the complexity of computing the free distance is discussed and a counterexample to a conjecture on the relationship of row distance to free distance for systematic codes Ìs presented. Finally, an improved Gilbert bound for definite decoding is derived.
A Note On The Free Distance Of A Convolutional Code, Alexander Miczo
A Note On The Free Distance Of A Convolutional Code, Alexander Miczo
Electrical Engineering and Computer Science - Technical Reports
A counterexample to a conjecture on the number of constraint lengths required to achieve the free distance of a rate l/n systematic convolutional code is presented.
Generalized Threshold Decoding Of Convolutional Codes, Luther D. Rudolph
Generalized Threshold Decoding Of Convolutional Codes, Luther D. Rudolph
Electrical Engineering and Computer Science - Technical Reports
It is shown that any rate l/b systematic convolutional code over GF(p) can be decoded up to its minimum distance with respect to the decoding constraint length by a one-step threshold decoder. It is further shown that this decoding method can be generalized in a natural way to allow “decoding” of a received sequence in its unquantized analog form.