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New cubic self-dual codes of length 54, 60 and 66
We study the construction of quasi-cyclic self-dual codes, especially of
binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell
with the algebraic approach of [9]. In particular, we improve the previous
results by constructing 1 new binary [54, 27, 10], 6 new [60, 30, 12] and 50
new [66, 33, 12] cubic self-dual codes. We conjecture that there exist no more
binary cubic self-dual codes with length 54, 60 and 66.Comment: 8 page
QPSK Block-Modulation Codes for Unequal Error Protection
Unequal error protection (UEP) codes find applications in broadcast channels, as well as in other digital communication systems, where messages have different degrees of importance. Binary linear UEP (LUEP) codes combined with a Gray mapped QPSK signal set are used to obtain new efficient QPSK block-modulation codes for unequal error protection. Several examples of QPSK modulation codes that have the same minimum squared Euclidean distance as the best QPSK modulation codes, of the same rate and length, are given. In the new constructions of QPSK block-modulation codes, even-length binary LUEP codes are used. Good even-length binary LUEP codes are obtained when shorter binary linear codes are combined using either the well-known |uÂŻ|uÂŻ+vÂŻ|-construction or the so-called construction X. Both constructions have the advantage of resulting in optimal or near-optimal binary LUEP codes of short to moderate lengths, using very simple linear codes, and may be used as constituent codes in the new constructions. LUEP codes lend themselves quite naturally to multistage decoding up to their minimum distance, using the decoding of component subcodes. A new suboptimal two-stage soft-decision decoding of LUEP codes is presented and its application to QPSK block-modulation codes for UEP illustrated
New binary and ternary LCD codes
LCD codes are linear codes with important cryptographic applications.
Recently, a method has been presented to transform any linear code into an LCD
code with the same parameters when it is supported on a finite field with
cardinality larger than 3. Hence, the study of LCD codes is mainly open for
binary and ternary fields. Subfield-subcodes of -affine variety codes are a
generalization of BCH codes which have been successfully used for constructing
good quantum codes. We describe binary and ternary LCD codes constructed as
subfield-subcodes of -affine variety codes and provide some new and good LCD
codes coming from this construction
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