Error-Correcting Codes from Higher-Dimensional Varieties

Error-Correcting Codes from higher-dimensional varieties

In this paper we use intersection theory to develop methods for obtaining lower bounds on the parameters of algebraic geometric error-correcting codes constructed from varieties of arbitrary dimension. The methods are sufficiently general to encompass many of the codes previously constructed from higherdimensional varieties, as well as those coming from curves. And still, the bounds obtained ar...

Codes from Higher - Dimensional Varieties

Algebraic geometry codes from higher dimensional varieties

This paper is a general survey of work on Goppa-type codes from higher dimensional algebraic varieties. The construction and several techniques for estimating the minimum distance are described first. Codes from various classes of varieties, including Hermitian hypersurfaces, Grassmannians, flag varieties, ruled surfaces over curves, and Deligne-Lusztig varieties are considered. Connections wit...

Error-correcting two-dimensional modulation codes

Modulation coding, to limit the number of consecutive zeroes in a data stream, is essential in digital magnetic recording/playback systems. Additionally, such sys­ tems require error correction coding to ensure that the decoded output matches the recorder input, even if noise is present. Typically these two coding steps have been performed independently, although various methods of combining th...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...