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List decoding of a class of affine variety codes

Consider a polynomial F in m variables and a finite point ensemble S = S1 × · · · × Sm. When given the leading monomial of F with respect to a lexicographic ordering we derive improved information on the possible number of zeros of F of multiplicity at least r from S. We then use this information to design a list decoding algorithm for a large class of affine variety codes.

Multiple class G-networks with list-oriented deletions

We study a new dynamic of generalized networks of queues. We consider networks with multiple classes of customers and signals, and three types of service disciplines: FIFO, LIFO/PR and Processor Sharing. Moreover, we consider a probabilistic deleting mechanism based on iterated deletions of customers according to an arbitrary list of service stations. We prove that these networks have a steady-...

Optimal rate algebraic list decoding using narrow ray class fields

We use class field theory, specifically Drinfeld modules of rank 1, to construct a family of asymptotically good algebraic-geometric (AG) codes over fixed alphabets. Over a field of size l, these codes are within 2/( √ l − 1) of the Singleton bound. The functions fields underlying these codes are subfields with a cyclic Galois group of the narrow ray class field of certain function fields. The ...

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