scholarly journals Construction of Linear Codes over Rings Zm Correcting Double ±1 or ±2 Errors

2018 ◽  
pp. 66-73
Author(s):  
Gurgen Khachatrian ◽  
Hamlet Khachatrian
Keyword(s):  
Linear Codes ◽  
Codes Over Rings ◽  
Optimal Codes ◽  
Absolute Value ◽  
Linear Codes Over Rings

In this paper a construction of double ±1 and ±2 errors correcting linear optimal and quasi-optimal codes over rings Z5, Z7 and Z9 is presented with the limitation that both errors have the same amplitude in absolute value.

Quantum codes over rings

2014 ◽  
Vol 12 (04) ◽  
pp. 1450020 ◽  
Author(s):  
Kenza Guenda ◽  
T. Aaron Gulliver
Keyword(s):  
Linear Codes ◽  
Error Correcting Codes ◽  
Codes Over Rings ◽  
Quantum Codes ◽  
Matrix Product ◽  
Frobenius Rings ◽  
Linear Codes Over Rings ◽  
Generalized Gray Map ◽  
Css Construction ◽  
Quantum Error

This paper considers the construction of quantum error correcting codes from linear codes over finite commutative Frobenius rings. We extend the Calderbank–Shor–Steane (CSS) construction to these rings. Further, quantum codes are extended to matrix product codes. Quantum codes over 𝔽pk are also obtained from linear codes over rings using the generalized Gray map.

Weights modulo p e of linear codes over rings

2007 ◽  
Vol 43 (2-3) ◽  
pp. 147-165 ◽  
Author(s):  
Bahattin Yildiz
Keyword(s):  
Linear Codes ◽  
Codes Over Rings ◽  
Modulo P ◽  
Linear Codes Over Rings

On modules with cyclic socle

2016 ◽  
Vol 15 (09) ◽  
pp. 1650162 ◽  
Author(s):  
Ali Assem
Keyword(s):  
Coding Theory ◽  
Linear Codes ◽  
Extension Theorem ◽  
Extension Property ◽  
Codes Over Rings ◽  
Extension Problem ◽  
Hamming Weight ◽  
Frobenius Rings ◽  
Code Equivalence ◽  
Open Question

The extension problem for linear codes over modules with respect to Hamming weight was already settled in [J. A. Wood, Code equivalence characterizes finite Frobenius rings, Proc. Amer. Math. Soc. 136 (2008) 699–706; Foundations of linear codes defined over finite modules: The extension theorem and MacWilliams identities, in Codes Over Rings, Series on Coding Theory and Cryptology, Vol. 6 (World Scientific, Singapore, 2009), pp. 124–190]. A similar problem arises naturally with respect to symmetrized weight compositions (SWC). In 2009, Wood proved that Frobenius bimodules have the extension property (EP) for SWC. More generally, in [N. ElGarem, N. Megahed and J. A. Wood, The extension theorem with respect to symmetrized weight compositions, in 4th Int. Castle Meeting on Coding Theory and Applications (2014)], it is shown that having a cyclic socle is sufficient for satisfying the property, while the necessity remained an open question. Here, landing in midway, a partial converse is proved. For a (not small) class of finite module alphabets, the cyclic socle is shown necessary to satisfy the EP. The idea is bridging to the case of Hamming weight through a new weight function. Note: All rings are finite with unity, and all modules are finite too. This may be re-emphasized in some statements. The convention for left homomorphisms is that inputs are to the left.

Regional Frontal Lobe Response Magnitudes During Affective Shifting Covary With Resting Heart Rate Variability in Healthy Volunteers

2016 ◽  
Vol 30 (4) ◽  
pp. 165-174 ◽  
Author(s):  
Ryan Smith ◽  
John J.B. Allen ◽  
Julian F. Thayer ◽  
Richard D. Lane
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Healthy Subjects ◽  
Emotional Reactivity ◽  
Bold Signal ◽  
Resting Heart Rate ◽  
Functional Magnetic Resonance ◽  
Absolute Value ◽  
Cardiac Vagal Control ◽  
Resting Heart Rate Variability

Abstract. We hypothesized that in healthy subjects differences in resting heart rate variability (rHRV) would be associated with differences in emotional reactivity within the medial visceromotor network (MVN). We also probed whether this MVN-rHRV relationship was diminished in depression. Eleven healthy adults and nine depressed subjects performed the emotional counting stroop task in alternating blocks of emotion and neutral words during functional magnetic resonance imaging (fMRI). The correlation between rHRV outside the scanner and BOLD signal reactivity (absolute value of change between adjacent blocks in the BOLD signal) was examined in specific MVN regions. Significant negative correlations were observed between rHRV and average BOLD shift magnitude (BSM) in several MVN regions in healthy subjects but not depressed subjects. This preliminary report provides novel evidence relating emotional reactivity in MVN regions to rHRV. It also provides preliminary suggestive evidence that depression may involve reduced interaction between the MVN and cardiac vagal control.

Relation of Statistically Significant, Abnormal, and Typical WAIS-R VIQ-PIQ Discrepancies to Full Scale IQs

2000 ◽  
Vol 16 (2) ◽  
pp. 107-114 ◽  
Author(s):  
Louis M. Hsu ◽  
Judy Hayman ◽  
Judith Koch ◽  
Debbie Mandell
Keyword(s):  
Graphical Method ◽  
The United States ◽  
Full Scale ◽  
True Score ◽  
Absolute Value ◽  
Normative Population ◽  
The Us ◽  
The Mean ◽  
And Performance ◽  
Quadratic Models

Summary: In the United States' normative population for the WAIS-R, differences (Ds) between persons' verbal and performance IQs (VIQs and PIQs) tend to increase with an increase in full scale IQs (FSIQs). This suggests that norm-referenced interpretations of Ds should take FSIQs into account. Two new graphs are presented to facilitate this type of interpretation. One of these graphs estimates the mean of absolute values of D (called typical D) at each FSIQ level of the US normative population. The other graph estimates the absolute value of D that is exceeded only 5% of the time (called abnormal D) at each FSIQ level of this population. A graph for the identification of conventional “statistically significant Ds” (also called “reliable Ds”) is also presented. A reliable D is defined in the context of classical true score theory as an absolute D that is unlikely (p < .05) to be exceeded by a person whose true VIQ and PIQ are equal. As conventionally defined reliable Ds do not depend on the FSIQ. The graphs of typical and abnormal Ds are based on quadratic models of the relation of sizes of Ds to FSIQs. These models are generalizations of models described in Hsu (1996) . The new graphical method of identifying Abnormal Ds is compared to the conventional Payne-Jones method of identifying these Ds. Implications of the three juxtaposed graphs for the interpretation of VIQ-PIQ differences are discussed.

High-precision Absolute Value Measurement of Reflection by Time Domain OCT

2018 ◽  
Vol 138 (5) ◽  
pp. 198-203
Author(s):  
Masayuki Tanaka ◽  
Tatsuo Shiina
Keyword(s):  
High Precision ◽  
Time Domain ◽  
Absolute Value ◽  
Value Measurement ◽  
Time Domain Oct

A Class of Left Dihedral Codes Over Rings $\mathbb{F}_q+u\mathbb{F}_q$

2017 ◽  
Vol E100.A (12) ◽  
pp. 2585-2593
Author(s):  
Yuan CAO ◽  
Yonglin CAO ◽  
Jian GAO
Keyword(s):  
Codes Over Rings ◽  
Dihedral Codes
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