3,588 research outputs found
The hull of two classical propagation rules and their applications
Propagation rules are of great help in constructing good linear codes. Both
Euclidean and Hermitian hulls of linear codes perform an important part in
coding theory. In this paper, we consider these two aspects together and
determine the dimensions of Euclidean and Hermitian hulls of two classical
propagation rules, namely, the direct sum construction and the
-construction. Some new criteria for resulting codes
derived from these two propagation rules being self-dual, self-orthogonal or
linear complement dual (LCD) codes are given. As applications, we construct
some linear codes with prescribed hull dimensions and many new binary, ternary
Euclidean formally self-dual (FSD) LCD codes, quaternary Hermitian FSD LCD
codes and good quaternary Hermitian LCD codes which are optimal or have best or
almost best known parameters according to Datebase at
. Moreover, our methods contributes positively to
improve the lower bounds on the minimum distance of known LCD codes.Comment: 16 pages, 5 table
Convolutional and tail-biting quantum error-correcting codes
Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to
4096 states and minimum distances up to 10 are constructed as stabilizer codes
from classical self-orthogonal rate-1/n F_4-linear and binary linear
convolutional codes, respectively. These codes generally have higher rate and
less decoding complexity than comparable quantum block codes or previous
quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same
rate and error-correction capability and essentially the same decoding
algorithms are derived from these convolutional codes via tail-biting.Comment: 30 pages. Submitted to IEEE Transactions on Information Theory. Minor
revisions after first round of review
Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes
Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum
convolutional codes are constructed from classical self-orthogonal
\F_4-linear and \F_2-linear convolutional codes, respectively. These
quantum convolutional codes have higher rate than comparable quantum block
codes or previous quantum convolutional codes, and are simple to decode. A
block single-error-correcting [9, 3, 3] tail-biting code is derived from the
unrestricted convolutional code, and similarly a [15, 5, 3] CSS-type block code
from the CSS-type convolutional code.Comment: 5 pages; to appear in Proceedings of 2005 IEEE International
Symposium on Information Theor
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