71,144 research outputs found
Asymptotically Good Additive Cyclic Codes Exist
Long quasi-cyclic codes of any fixed index have been shown to be
asymptotically good, depending on Artin primitive root conjecture in (A.
Alahmadi, C. G\"uneri, H. Shoaib, P. Sol\'e, 2017). We use this recent result
to construct good long additive cyclic codes on any extension of fixed degree
of the base field. Similarly self-dual double circulant codes, and self-dual
four circulant codes, have been shown to be good, also depending on Artin
primitive root conjecture in (A. Alahmadi, F. \"Ozdemir, P. Sol\'e, 2017) and (
M. Shi, H. Zhu, P. Sol\'e, 2017) respectively. Building on these recent
results, we can show that long cyclic codes are good over \F_q, for many
classes of 's. This is a partial solution to a fifty year old open problem
On the symmetry of good nonlinear codes
It is shown that there are arbitrarily long "good" (in the sense of Gilbert) binary block codes that are preserved under very large permutation groups. This result contrasts sharply with the properties of linear codes: it is conjectured that long cyclic codes are bad, and known that long affine-invariant codes are bad
Higher-order CIS codes
We introduce {\bf complementary information set codes} of higher-order. A
binary linear code of length and dimension is called a complementary
information set code of order (-CIS code for short) if it has
pairwise disjoint information sets. The duals of such codes permit to reduce
the cost of masking cryptographic algorithms against side-channel attacks. As
in the case of codes for error correction, given the length and the dimension
of a -CIS code, we look for the highest possible minimum distance. In this
paper, this new class of codes is investigated. The existence of good long CIS
codes of order is derived by a counting argument. General constructions
based on cyclic and quasi-cyclic codes and on the building up construction are
given. A formula similar to a mass formula is given. A classification of 3-CIS
codes of length is given. Nonlinear codes better than linear codes are
derived by taking binary images of -codes. A general algorithm based on
Edmonds' basis packing algorithm from matroid theory is developed with the
following property: given a binary linear code of rate it either provides
disjoint information sets or proves that the code is not -CIS. Using
this algorithm, all optimal or best known codes where and are shown to be -CIS for all
such and , except for with and with .Comment: 13 pages; 1 figur
A STUDY OF LINEAR ERROR CORRECTING CODES
Since Shannon's ground-breaking work in 1948, there have been two main development streams
of channel coding in approaching the limit of communication channels, namely classical coding
theory which aims at designing codes with large minimum Hamming distance and probabilistic
coding which places the emphasis on low complexity probabilistic decoding using long codes built
from simple constituent codes. This work presents some further investigations in these two channel
coding development streams.
Low-density parity-check (LDPC) codes form a class of capacity-approaching codes with sparse
parity-check matrix and low-complexity decoder Two novel methods of constructing algebraic binary
LDPC codes are presented. These methods are based on the theory of cyclotomic cosets, idempotents
and Mattson-Solomon polynomials, and are complementary to each other. The two methods
generate in addition to some new cyclic iteratively decodable codes, the well-known Euclidean and
projective geometry codes. Their extension to non binary fields is shown to be straightforward.
These algebraic cyclic LDPC codes, for short block lengths, converge considerably well under iterative
decoding. It is also shown that for some of these codes, maximum likelihood performance may
be achieved by a modified belief propagation decoder which uses a different subset of 7^ codewords
of the dual code for each iteration.
Following a property of the revolving-door combination generator, multi-threaded minimum
Hamming distance computation algorithms are developed. Using these algorithms, the previously
unknown, minimum Hamming distance of the quadratic residue code for prime 199 has been evaluated.
In addition, the highest minimum Hamming distance attainable by all binary cyclic codes
of odd lengths from 129 to 189 has been determined, and as many as 901 new binary linear codes
which have higher minimum Hamming distance than the previously considered best known linear
code have been found.
It is shown that by exploiting the structure of circulant matrices, the number of codewords
required, to compute the minimum Hamming distance and the number of codewords of a given
Hamming weight of binary double-circulant codes based on primes, may be reduced. A means
of independently verifying the exhaustively computed number of codewords of a given Hamming
weight of these double-circulant codes is developed and in coiyunction with this, it is proved that
some published results are incorrect and the correct weight spectra are presented. Moreover, it is
shown that it is possible to estimate the minimum Hamming distance of this family of prime-based
double-circulant codes.
It is shown that linear codes may be efficiently decoded using the incremental correlation Dorsch
algorithm. By extending this algorithm, a list decoder is derived and a novel, CRC-less error detection
mechanism that offers much better throughput and performance than the conventional ORG
scheme is described. Using the same method it is shown that the performance of conventional CRC
scheme may be considerably enhanced. Error detection is an integral part of an incremental redundancy
communications system and it is shown that sequences of good error correction codes,
suitable for use in incremental redundancy communications systems may be obtained using the
Constructions X and XX. Examples are given and their performances presented in comparison to
conventional CRC schemes
Recommendation for Creep and Creep-fatigue assessment for P91 Components
This report is based on the results and experience gained in assessing both public domain and MATTER data, some previously reported in the MATTER deliverable D4.5: “Creep-fatigue interaction rules for P91” and some assessed here. A number of methods, including interaction diagram based methods and simplified methods, have been compared for predicting the creep-fatigue life of P91 steel. The effect of cyclic softening on creep properties have been considered in the evaluations presented in this report. The purpose of this report is to give recommendations for creep and creep-fatigue assessment for components made of X10CrMoVNb9-1 (P91) steel. Based on the
conclusions of the assessments the following recommendations are given:
1.The creep properties of P91 steel suffer from cyclic loading and it is recommended that the current RCC-MRx creep strain equations should be modified or replaced by a model that can implement time factors or stress reduction factors to correct for softening. Suitable models have been identified. The softening of P91 potentially causes unconservativeness in significant creep conditions where accumulated strain is a limiting design factor.
2.The interaction diagram models currently applied in design codes are complicated to apply and include several complex modelling challenges. It has been recommended that alternative modelling concepts, such as using simplified models should be considered for use in design codes. The simplified models optimized for P91 have been shown to give good and robust predictions on cycles to failure.
3.Currently available P91 data mainly consists of large strain range and short hold period data, where creep is mainly causing additional strain. Data with verified creep cavitation damage is limited or totally lacking. It is recommended that more data is generated at low strain ranges and long hold times to improve long term extrapolation robustness. Tensile property data for softened material is also needed to determine the stress range where power-law breakdown behaviour in creep can be expected and to improve the understanding of the long term microstructural evolution in cyclic service.JRC.F.4-Innovative Technologies for Nuclear Reactor Safet
Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound
We prove that there exist non-linear binary cyclic codes that attain the
Gilbert-Varshamov bound
Low-complexity quantum codes designed via codeword-stabilized framework
We consider design of the quantum stabilizer codes via a two-step,
low-complexity approach based on the framework of codeword-stabilized (CWS)
codes. In this framework, each quantum CWS code can be specified by a graph and
a binary code. For codes that can be obtained from a given graph, we give
several upper bounds on the distance of a generic (additive or non-additive)
CWS code, and the lower Gilbert-Varshamov bound for the existence of additive
CWS codes. We also consider additive cyclic CWS codes and show that these codes
correspond to a previously unexplored class of single-generator cyclic
stabilizer codes. We present several families of simple stabilizer codes with
relatively good parameters.Comment: 12 pages, 3 figures, 1 tabl
Binary Cyclic Codes from Explicit Polynomials over \gf(2^m)
Cyclic codes are a subclass of linear codes and have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, monomials and
trinomials over finite fields with even characteristic are employed to
construct a number of families of binary cyclic codes. Lower bounds on the
minimum weight of some families of the cyclic codes are developed. The minimum
weights of other families of the codes constructed in this paper are
determined. The dimensions of the codes are flexible. Some of the codes
presented in this paper are optimal or almost optimal in the sense that they
meet some bounds on linear codes. Open problems regarding binary cyclic codes
from monomials and trinomials are also presented.Comment: arXiv admin note: substantial text overlap with arXiv:1206.4687,
arXiv:1206.437
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