76,292 research outputs found
Some new results on the self-dual [120,60,24] code
The existence of an extremal self-dual binary linear code of length 120 is a
long-standing open problem. We continue the investigation of its automorphism
group, proving that automorphisms of order 30 and 57 cannot occur. Supposing
the involutions acting fixed point freely, we show that also automorphisms of
order 8 cannot occur and the automorphism group is of order at most 120, with
further restrictions. Finally, we present some necessary conditions for the
existence of the code, based on shadow and design theory.Comment: 23 pages, 6 tables, to appear in Finite Fields and Their Application
Coherence Optimization and Best Complex Antipodal Spherical Codes
Vector sets with optimal coherence according to the Welch bound cannot exist
for all pairs of dimension and cardinality. If such an optimal vector set
exists, it is an equiangular tight frame and represents the solution to a
Grassmannian line packing problem. Best Complex Antipodal Spherical Codes
(BCASCs) are the best vector sets with respect to the coherence. By extending
methods used to find best spherical codes in the real-valued Euclidean space,
the proposed approach aims to find BCASCs, and thereby, a complex-valued vector
set with minimal coherence. There are many applications demanding vector sets
with low coherence. Examples are not limited to several techniques in wireless
communication or to the field of compressed sensing. Within this contribution,
existing analytical and numerical approaches for coherence optimization of
complex-valued vector spaces are summarized and compared to the proposed
approach. The numerically obtained coherence values improve previously reported
results. The drawback of increased computational effort is addressed and a
faster approximation is proposed which may be an alternative for time critical
cases
Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound
A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and it is shown that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F-q, for all squares q = l(2). It is also shown that self-orthogonal and self-dual codes attain the Tsfasman-Vladut-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower E-0 subset of E-1 subset of E-2 subset of center dot center dot center dot of function fields over F-q (with q = l(2)), where all extensions E-n/E-0 are Galois
A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes
In this paper, we study the impact of locality on the decoding of binary
cyclic codes under two approaches, namely ordered statistics decoding (OSD) and
trellis decoding. Given a binary cyclic code having locality or availability,
we suitably modify the OSD to obtain gains in terms of the Signal-To-Noise
ratio, for a given reliability and essentially the same level of decoder
complexity. With regard to trellis decoding, we show that careful introduction
of locality results in the creation of cyclic subcodes having lower maximum
state complexity. We also present a simple upper-bounding technique on the
state complexity profile, based on the zeros of the code. Finally, it is shown
how the decoding speed can be significantly increased in the presence of
locality, in the moderate-to-high SNR regime, by making use of a quick-look
decoder that often returns the ML codeword.Comment: Extended version of a paper submitted to ISIT 201
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