903 research outputs found
The q-ary image of some qm-ary cyclic codes: permutation group and soft-decision decoding
Using a particular construction of generator matrices of
the q-ary image of qm-ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups. The equivalence of such codes with some two-dimensional (2-D) Abelian codes and cyclic codes is deduced from this property. These permutations are also used in the area of the soft-decision decoding of some expanded Reed–Solomon (RS) codes to improve the performance of generalized minimum-distance decoding
Cyclic LRC Codes and their Subfield Subcodes
We consider linear cyclic codes with the locality property, or locally
recoverable codes (LRC codes). A family of LRC codes that generalizes the
classical construction of Reed-Solomon codes was constructed in a recent paper
by I. Tamo and A. Barg (IEEE Transactions on Information Theory, no. 8, 2014;
arXiv:1311.3284). In this paper we focus on the optimal cyclic codes that arise
from the general construction. We give a characterization of these codes in
terms of their zeros, and observe that there are many equivalent ways of
constructing optimal cyclic LRC codes over a given field. We also study
subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish
several results about their locality and minimum distance.Comment: Submitted for publicatio
Cyclic LRC Codes, binary LRC codes, and upper bounds on the distance of cyclic codes
We consider linear cyclic codes with the locality property, or locally
recoverable codes (LRC codes). A family of LRC codes that generalize the
classical construction of Reed-Solomon codes was constructed in a recent paper
by I. Tamo and A. Barg (IEEE Trans. Inform. Theory, no. 8, 2014). In this paper
we focus on optimal cyclic codes that arise from this construction. We give a
characterization of these codes in terms of their zeros, and observe that there
are many equivalent ways of constructing optimal cyclic LRC codes over a given
field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes)
and establish several results about their locality and minimum distance. The
locality parameter of a cyclic code is related to the dual distance of this
code, and we phrase our results in terms of upper bounds on the dual distance.Comment: 12pp., submitted for publication. An extended abstract of this
submission was posted earlier as arXiv:1502.01414 and was published in
Proceedings of the 2015 IEEE International Symposium on Information Theory,
Hong Kong, China, June 14-19, 2015, pp. 1262--126
Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound
It was shown by Massey that linear complementary dual (LCD for short) codes
are asymptotically good. In 2004, Sendrier proved that LCD codes meet the
asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound
still remains to be the best asymptotical lower bound for LCD codes. In this
paper, we show that an algebraic geometry code over a finite field of even
characteristic is equivalent to an LCD code and consequently there exists a
family of LCD codes that are equivalent to algebraic geometry codes and exceed
the asymptotical GV bound
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