8,344 research outputs found
Gatekeepers and lock masters: the control of access in the Neo-Assyrian palaces
Book description: This volume is intended as a tribute to the memory of the Sumerologist Jeremy Black, who died in 2004. The Sumerian phrase, âYour praise is sweetâ is commonly addressed to a deity at the close of a work of Sumerian literature. The scope of the thirty contributions, from Sumerology to the nineteenth-century rediscovery of Mesopotamia, is testament to Jeremyâs own wide-ranging interests and to his ability to forge scholarly connections and friendships among all who shared his interest in ancient Iraq
Special Libraries, October 1959
Volume 50, Issue 8https://scholarworks.sjsu.edu/sla_sl_1959/1007/thumbnail.jp
Special Libraries, April 1956
Volume 47, Issue 4https://scholarworks.sjsu.edu/sla_sl_1956/1003/thumbnail.jp
Syndrome decoding of Reed-Muller codes and tensor decomposition over finite fields
Reed-Muller codes are some of the oldest and most widely studied
error-correcting codes, of interest for both their algebraic structure as well
as their many algorithmic properties. A recent beautiful result of Saptharishi,
Shpilka and Volk showed that for binary Reed-Muller codes of length and
distance , one can correct random errors
in time (which is well beyond the worst-case error
tolerance of ).
In this paper, we consider the problem of `syndrome decoding' Reed-Muller
codes from random errors. More specifically, given the
-bit long syndrome vector of a codeword corrupted in
random coordinates, we would like to compute the
locations of the codeword corruptions. This problem turns out to be equivalent
to a basic question about computing tensor decomposition of random low-rank
tensors over finite fields.
Our main result is that syndrome decoding of Reed-Muller codes (and the
equivalent tensor decomposition problem) can be solved efficiently, i.e., in
time. We give two algorithms for this problem:
1. The first algorithm is a finite field variant of a classical algorithm for
tensor decomposition over real numbers due to Jennrich. This also gives an
alternate proof for the main result of Saptharishi et al.
2. The second algorithm is obtained by implementing the steps of the
Berlekamp-Welch-style decoding algorithm of Saptharishi et al. in
sublinear-time. The main new ingredient is an algorithm for solving certain
kinds of systems of polynomial equations.Comment: 24 page
Phased burst error-correcting array codes
Various aspects of single-phased burst-error-correcting array codes are explored. These codes are composed of two-dimensional arrays with row and column parities with a diagonally cyclic readout order; they are capable of correcting a single burst error along one diagonal. Optimal codeword sizes are found to have dimensions n1Ăn2 such that n2 is the smallest prime number larger than n1. These codes are capable of reaching the Singleton bound. A new type of error, approximate errors, is defined; in q-ary applications, these errors cause data to be slightly corrupted and therefore still close to the true data level. Phased burst array codes can be tailored to correct these codes with even higher rates than befor
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