Generalized Subspace Subcodes With Application in Cryptology

Generalized subspace subcodes with application in cryptology

Most of the codes that have an algebraic decoding algorithm are derived from the Reed Solomon codes. They are obtained by taking equivalent codes, for example the generalized Reed Solomon codes, or by using the so-called subfield subcode method, which leads to Alternant codes and Goppa codes over the underlying prime field, or over some intermediate subfield. The main advantages of these constr...

Subspace Subcodes of Reed-Solomon Codes

space subcode of a Reed-Solomon (SSRS) code Over GF(2"') is the set of RS codewords, whose components all lie in a particular GF(2)subspace of GF(2"). SSRS codes include both generalized B C H codes and "trace-shortened" Rs codes [2][3] as special casea. In this paper we present an explicit formula for t h e dimension of an arbitrary RS subspace subcode. Using this formula, we And that in many ...

Properties of subspace subcodes of optimum codes in rank metric

Maximum rank distance codes denoted MRD-codes are the equivalent in rank metric of MDS-codes. Given any integer $q$ power of a prime and any integer $n$ there is a family of MRD-codes of length $n$ over $\FF{q^n}$ having polynomial-time decoding algorithms. These codes can be seen as the analogs of Reed-Solomon codes (hereafter denoted RS-codes) for rank metric. In this paper their subspace sub...

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Generalized URV Subspace Tracking

The convergence rate of the Least Mean Squares (LMS) algorithm is poor whenever the adaptive lter input auto-correlation matrix is ill-conditioned. In this paper we propose a new LMS algorithm to alleviate this problem. It uses a data dependent signal transformation. The algorithm tracks the subspaces corresponding to clusters of eigenvalues of the auto-correlation matrix of the input to the ad...