24,628 research outputs found
New Constant-Weight Codes from Propagation Rules
This paper proposes some simple propagation rules which give rise to new
binary constant-weight codes.Comment: 4 page
A class of punctured simplex codes which are proper for error detection
Binary linear [n,k] codes that are proper for error detection are known for
many combinations of n and k. For the remaining combinations, existence of
proper codes is conjectured. In this paper, a particular class of [n,k] codes
is studied in detail. In particular, it is shown that these codes are proper
for many combinations of n and k which were previously unsettled
Communication Cost for Updating Linear Functions when Message Updates are Sparse: Connections to Maximally Recoverable Codes
We consider a communication problem in which an update of the source message
needs to be conveyed to one or more distant receivers that are interested in
maintaining specific linear functions of the source message. The setting is one
in which the updates are sparse in nature, and where neither the source nor the
receiver(s) is aware of the exact {\em difference vector}, but only know the
amount of sparsity that is present in the difference-vector. Under this
setting, we are interested in devising linear encoding and decoding schemes
that minimize the communication cost involved. We show that the optimal
solution to this problem is closely related to the notion of maximally
recoverable codes (MRCs), which were originally introduced in the context of
coding for storage systems. In the context of storage, MRCs guarantee optimal
erasure protection when the system is partially constrained to have local
parity relations among the storage nodes. In our problem, we show that optimal
solutions exist if and only if MRCs of certain kind (identified by the desired
linear functions) exist. We consider point-to-point and broadcast versions of
the problem, and identify connections to MRCs under both these settings. For
the point-to-point setting, we show that our linear-encoder based achievable
scheme is optimal even when non-linear encoding is permitted. The theory is
illustrated in the context of updating erasure coded storage nodes. We present
examples based on modern storage codes such as the minimum bandwidth
regenerating codes.Comment: To Appear in IEEE Transactions on Information Theor
An investigation of error correcting techniques for OMV data
Papers on the following topics are presented: considerations of testing the Orbital Maneuvering Vehicle (OMV) system with CLASS; OMV CLASS test results (first go around); equivalent system gain available from R-S encoding versus a desire to lower the power amplifier from 25 watts to 20 watts for OMV; command word acceptance/rejection rates for OMV; a memo concerning energy-to-noise ratio for the Viterbi-BSC Channel and the impact of Manchester coding loss; and an investigation of error correcting techniques for OMV and Advanced X-ray Astrophysics Facility (AXAF)
An experimental and finite element study of the low-cycle fatigue failure of a galvanised steel lighting column
This paper presents the results of a low-cycle fatigue test on a lighting column. The wind induced vibration phenomena responsible for low cycle fatigue in such structures is discussed and the failure mechanism is examined. It was initially thought that poor quality weld detail was the major influence on the fatigue life of such columns. However, the significant role of the galvanised coating in the failure process is also highlighted. The experimental results are compared with those from a detailed 3D finite element model. Various methods of calculating hot-spot stresses at welded joints are examined and use of a simple peak stress removal approach is shown to produce significantly different values compared with the other methods examined
Bounds on Binary Locally Repairable Codes Tolerating Multiple Erasures
Recently, locally repairable codes has gained significant interest for their
potential applications in distributed storage systems. However, most
constructions in existence are over fields with size that grows with the number
of servers, which makes the systems computationally expensive and difficult to
maintain. Here, we study linear locally repairable codes over the binary field,
tolerating multiple local erasures. We derive bounds on the minimum distance on
such codes, and give examples of LRCs achieving these bounds. Our main
technical tools come from matroid theory, and as a byproduct of our proofs, we
show that the lattice of cyclic flats of a simple binary matroid is atomic.Comment: 9 pages, 1 figure. Parts of this paper were presented at IZS 2018.
This extended arxiv version includes corrected versions of Theorem 1.4 and
Proposition 6 that appeared in the IZS 2018 proceeding
Some -designs and shortened codes from binary cyclic codes with three zeros
Linear codes and -designs are interactive with each other. It is well
known that some -designs have been constructed by using certain linear codes
in recent years. However, only a small number of infinite families of the
extended codes of linear codes holding an infinite family of -designs with
are reported in the literature. In this paper, we study the extended
codes of the augmented codes of a class of binary cyclic codes with three zeros
and their dual codes, and show that those codes hold -designs. Furthermore,
we obtain some shortened codes from the studied cyclic codes and explicitly
determine their parameters. Some of those shortened codes are optimal or almost
optimal.Comment: 20 pages. arXiv admin note: text overlap with arXiv:2110.03881,
arXiv:2007.0592
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