48 research outputs found

    Some new results on the self-dual [120,60,24] code

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    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

    Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

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    Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map

    CAMAC bulletin: A publication of the ESONE Committee Issue #14 December 1975 [last pub. of series]

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    CAMAC is a means of interconnecting many peripheral devices through a digital data highway to a data processing device such as a computer

    Advanced information processing system: The Army fault tolerant architecture conceptual study. Volume 2: Army fault tolerant architecture design and analysis

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    Described here is the Army Fault Tolerant Architecture (AFTA) hardware architecture and components and the operating system. The architectural and operational theory of the AFTA Fault Tolerant Data Bus is discussed. The test and maintenance strategy developed for use in fielded AFTA installations is presented. An approach to be used in reducing the probability of AFTA failure due to common mode faults is described. Analytical models for AFTA performance, reliability, availability, life cycle cost, weight, power, and volume are developed. An approach is presented for using VHSIC Hardware Description Language (VHDL) to describe and design AFTA's developmental hardware. A plan is described for verifying and validating key AFTA concepts during the Dem/Val phase. Analytical models and partial mission requirements are used to generate AFTA configurations for the TF/TA/NOE and Ground Vehicle missions

    Self Dual Codes and the Indecomposable Building Blocks

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    Just like prime numbers are to integers, indecomposable codes are to self dual codes. This paper gives an explicit listing of the first few families of binary self dual codes, up to length 16. Binary self dual codes that are decomposable are given as a composition of indecomposable codes. The indecomposable codes are explicitly listed with generator matrices. The complete classifying process is outlined

    A cost and utility analysis of NIM/CAMAC standards and equipment for shuttle payload data acquisition and control systems. Volume 3: Tasks 3 and 4

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    The modifications for the Nuclear Instrumentation Modular (NIM) and Computer Automated Measurement Control (CAMAC) equipment, designed for ground based laboratory use, that would be required to permit its use in the Spacelab environments were determined. The cost of these modifications were estimated and the most cost effective approach to implementing them were identified. A shared equipment implementation in which the various Spacelab users draw their required complement of standard NIM and CAMAC equipment for a given flight from a common equipment pool was considered. The alternative approach studied was a dedicated equipment implementation in which each of the users is responsible for procuring either their own NIM/CAMAC equipment or its custom built equivalent

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum
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