Classification of the perfect codes in the ∞ -Lee metric

We introduce and study a common generalization of 1-error binary perfect codes and perfect single error correcting codes in Lee metric, namely perfect codes on products of paths of length 2 and of infinite length. Both existence and nonexistence results are given.

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Weighted perfect codes in Lee metric

Electronic Notes in Discrete Mathematics ◽

10.1016/j.endm.2009.07.079 ◽

2009 ◽

Vol 34 ◽

pp. 477-481

Author(s):

P. Dorbec ◽

S. Gravier ◽

I. Honkala ◽

M. Mollard

Keyword(s):

Perfect Codes ◽

Lee Metric

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bi-Byte correcting non-binary perfect codes

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830919500186 ◽

2019 ◽

Vol 11 (02) ◽

pp. 1950018

Author(s):

Vinod Tyagi ◽

Tarun Lata

Keyword(s):

Binary Codes ◽

Perfect Codes

Etzion [T. Etzion, Perfect byte correcting codes, IEEE Trans. Inform. Theory 44 (1998) 3140–3146.] has classified byte error correcting binary codes into five different categories with respect to the size of the byte. If a code is partitioned into [Formula: see text] equal byte of size say [Formula: see text] then [Formula: see text] or the size of bytes is [Formula: see text]. Alternatively if bytes are of different size say, [Formula: see text] then [Formula: see text]. The result was further modified by Tyagi and Sethi [V. Tyagi and A. Sethi, [Formula: see text]-Byte correcting perfect codes, Asian-Eur. J. Math. 7(1) (2014) 1–8.] and the classification of bytes was given with respect to size of the byte as well as length of the burst. We call such codes as [Formula: see text]-byte correcting perfect codes. Our aim in this paper is to find the possibilities for the existence of [Formula: see text]-byte correcting non-binary perfect codes.

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Note on the spectral classification of carbon stars in the photographic infrared region

Symposium - International Astronomical Union ◽

10.1017/s0074180900053080 ◽

1966 ◽

Vol 24 ◽

pp. 21-23

Author(s):

Y. Fujita

Keyword(s):

Infrared Region ◽

Spectral Classification ◽

Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

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